an intersection of means a set is its Intersection with the phi set power set off power set off power set off I have to prove that it will be four, how will it come? Brother, I started scratching my head, I had to do something. I don't understand, I will do it slowly. If I say so, your a belongs to capital A. So is this True or False? Yes, please answer and at any time no one It is a long session, isn't it? Don't feel demotivated that you're not making friends. You will go in the middle, see if this Your lecture is for three to four hours. something or the other, nothing or nothing, a lot to you The guy must have gone after studying, hi, how are you? Welcome everyone to the Uday youtube1 short lecture is on this particular channel But okay, so what am I going to do today? I'll be known by a lot of children. Not all children will know that I once Let me introduce myself, okay? My name is Hrithik Mishra and I am your Let me make you feel maths, okay so friend, today we What are we going to do today on the sets? Which is the first chapter of your class 11th. I'm going to finish it in one short, okay? Now my friend stays simple, one short I don't take lectures in such a way that I Quickly, quickly, quickly, everything was done And many things were not left in the middle. I'm promising you and once you Try trusting, okay, how to trust? I mean, take a lecture once and see it. Maybe you understood it or not, friend. Everything can be understood through just one short lecture. If it can work, I promise you today. That in this chapter I will tell you everything I will tell you from basic to advance and all I will tell you everything, skip anything in between. I will not do it just with this one video Complete Sets Chapter of your Class 11th I will complete it without any delay Let's start with one of the most important This chapter is from your class 11th and many more. I think the children might If there is a backlog, backlog means five months wasted. I wasted six months And then I come to this lecture. I will tell you that you don't need to take the load now. You have come to the right channel, here you will find every One short lecture of the chapter is about to be received It's too early, isn't it? Let's start. bhaiya class 11th one short for sets now man what is the set set what It is very simple, okay, collection of You call a collection of elements a set. Ho, what did you say to the collection of elements? What do people say? I'll give you a little Let me try to explain what starting There are a couple of slides, that's a little bit You will see a lot of English because We are going to study the definition of sets. Okay, let's quickly focus on these hours. mathematical language everything in this Universe Weather Living and Non Living Is What is called an object or an element? Whether it is a living thing or a non-living thing what I would call an object for Example: This bag is kept, this bottle is kept This is a TV, this is an AC. There is a board saying, this is me, we all are one objects are I understand okay a given Collection of objects is said to be well Defined if we can definitely say weather a given particular object belongs to the Correction or not is well defined. Shall I explain it to you in a moment, simple? What is a set? A well-defined collection of object is called a set as I Kaha object means something living This thing is non-living, I am an object to everyone. I agree, okay, if I do particular collect objects collection of What I would call a set of objects I will tell you, but here is a very important Word Collection of Collection of Well Defined Well-defined objects what will I say set I will say now this well I'll explain what defined means. For example, if I told you that brother I told you brother, odd number less than 15 What did I say, odd numbers less than 15? Will this be a set? Yes, this will be a set. Why if I tell you odd numbers Less than 15, so which ones come to your mind? Elements or objects come brother odd Number less than 15 it's your one okay is 3 is 5 is 7 is 9 is 11 done 13 done less than 15 said meaning 15 not including curlies smaller than 15 put brackets, put commas again I will say curly bracket, what do we call this? curly brackets okay curly brackets Placed objects or elements Collected and put a comma in between Diya friends, this is what we call a set and the set is represented by the set Friends, capital letters A B CD and more You can represent this well now. Why are there defined objects because those Odd number less than 15 for you, that's somewhere There must be a guy sitting in Australia Same thing happens for me too but what is not well I'll explain it to you if I ask you Speak Collection of Collection of the Most Most Beautiful People in India Collection Who to collect Most Beautiful People in India now brother who It is not necessary that she is beautiful for you. It is not necessary that she is beautiful to me. Beautiful for her, so is your collection. My collection will be different, theirs will be different. The collection will be separate brother, this is not just one set. Perhaps you understand the meaning of well defined. I must have come, okay, some more examples Let's see and you will understand better. okay the collection of all verbals in the The English alphabet is the set containing five Elements A E I O U If I speak to you Collection of all words in English Alphabets are fine, so it would be the same for everyone. It is the same A E I O U, so just them collected and written like this E I O U Iyo ok put curry brackets Write more elements or write objects two okay and represent it here Let b be clear from the set now such that Bhaiya The Collection of All Even Natural Numbers Less than 10 is the set simple thing if I Should I tell you about the collection of all the evens? Natural numbers less than 10 to even natural numbers Brother, what are the number less than 10? u 4 6 8 I have collected them I put the bracket on and it became my set. Okay, so what is a set collection of well defined objects those objects well What is not a set should now be defined Let's talk a little about that for example. The Collection of All the Beautiful Girls of India is not a set collection of all Beautiful Girls in India is not a set Because what is beautiful to you is beautiful to me. It's not beautiful that what is beautiful to me Not beautiful enough for you to like She doesn't like me, what I There is some such scene, right? Come on, my friend. Do you understand what well-defined means? So is the correction of all prime numbers Less than 20 then brother whose collection to make This is also a set of prime numbers less than 20. Why would it be so brother, which is a prime number for you Less than 20 is for me and for them There must be some brother who is Satan there. But it will happen for him too, do you understand? Now you guys understand the meaning of set. How do you represent your friends? There are two ways to pay attention, one is roster or tabular form and there is one Set builder or property method now What is the roster form? Curly bracketed Write down the distinct elements of the set Separate elements using curly brackets Write down the set, this is called roster. What is a Form Set Builder Form? well we talk about I will give you an example of the roster form. I am Bhaiya, Bhaiya is a collection of collections off multiple of 50 multiple of 50 off Multiple of 50 will this be a set Exactly how a set will represent Will you do it brother, what did I say, a set? This collection Let's rewrite this A collection of all multiples of 50 all multiple of 50 will this be a set There will be exactly one set representing a If we write and put curly brackets then it becomes 50 The multiple becomes 50, it becomes 100, what else? It will go brother, it will become 150, it will become 200, it will continue like this It will go on and on, it will never end So this is one Infinity What we do at Infikel Farm Are all the details in roster or tabular form? You will write all the elements separately and Set builder form will put curly brackets What do you understand from the example? This form will come, there will be many Babua It seems difficult to me, okay, which is my first I keep looking at you again and again brother, I love you I call you Babua and you probably say the same thing. Okay, anyway, so one or two questions. I will do it, you will understand what to do Okay, so what did Set A say? Is the roster form given? The roster form is given in the set brother what elements are in your set a is 1a 2a 3a 4 is 5 is 6 is 7 is 8 then put curry bracket This is in its own set builder form I have to write, now how will I write, pay a little attention Please note that there is not necessarily only one method and So what is the first way to pay attention to while writing? The first method is very easy, you wrote A set. You will write x is it true that x what did I say x Is that true x read this as we do This is how we read it: x is true That x is true, I understood that x is true that x is true that x is like that okay how is it Bhaiya, I will tell you right now that x is true. Lesson E: 7 and x Belong to Natural Numbers what did I say what did I say here What do you do in the set builder form? Instead of writing the elements, you write their characteristics. From that speciality we will understand that brother, this is this These are the elements, for example, if I I would have told you that brother x your service or service is less than and the natural number x is your or less than sen and is a natural number, then Babu, this is what will come to your mind or If it is a natural number and less than seven then 1 2 3 If only 4 5 6 7 comes then do not write the elements I wrote its property as elements. While writing, I wrote down his property, what a thing. I am sure I understand this and such You can also write brother, there are other ways to write. Mano and how did you write set A bhaiya x is True that x well you replace these two dots like this You can also write the same thing as yours. I like it better, I wish Okay, so x is true that x is a x is a Natural Number X is a natural Number less than less than and equal to Understanding from and equal to 7 and curly brackets came and what do you understand from here also From here also you are understanding the same thing, did this I am going to say that you can also write like this and Is x true that x is true x belongs to natural number and and x your x Are you bigger than the forest or like the forest? Smaller than equivalent intake or equivalent intake understood its meaning x is smaller than your sen or Seven times greater than or equal to one So these are different ways to get the same thing. Let's move ahead as you wish He said, look again, I have given it every day. If it is given in the form, you have to write set Given in roster form in builder form Babua, I have to write it in the set builder form. What will you do, just look at this first. try to understand 1 2 4 7 14 28 what Do they understand anything? Some special features are visible, even if none are visible No problem, I will tell you again, three-four questions. After doing this you get practice that How to write it, it is written in the roster form What have I done to represent the set? Brother, look at what you wrote, I understood it. What if these numbers are divisors of 28? What you see are all these numbers. All of them are divisors of 28, then 28 are factors of so what can you write x is true that x is what boss x is true that x is a divisor of x is a divisor x is a factor of factor of 20 8 x is true that x is a factor of 28 now If I tell you this, you will understand. Well, x 28 means one, it means two. Fur is 7 is 14 is 28 itself It happens that you understand, you can do it this way and Just keep watching, just set the roster. Form Roster Form means that which is in it elements or objects are written to put a comma and a curly bracket Understanding what's in a builder form Brother, look 2 4 8 16 32, did you understand anything special? I am getting it, I am not getting it Even if it comes, there is no problem, what will you write x It is true that x is true that x = 2n Write what Given I x = 2n not 2 to the power n 2 Power n where to pay attention to where where where n what is where n n your n What will be your less than brother 2 to the power 1 2 2 to the power of 2 4 2 to the power of 38 2 to the power of 4 16 2 to the power 5 32 so n is your this n is your This is between 1 and 5, so you can write it like this Sakte ho ver n n is equal and greater than 1 is equal and greater than sorry less than five And one more thing and n belong to natural I understood this thing about natural numbers. Why is it necessary to write if I talk to you? If I only wrote this, Brother One and Fav There are many numbers in between Just between one and five, brother 1.1 1.2 1.3 so if you just write Meaning the value of n is decimal fraction irrational The number can be anything but as soon as you If you write belongs to natural number then Boss, you have made it clear here what you did. Key natural numbers only means one and five one or five or the natural numbers between them You have to take them, if you understand then it is yours One way of writing has become clear, let's go Next let's see what you are saying brother See Set D. The set is given in roster form. Do you understand what to write in the builder form? Look at this -6 -4 -2 0 2 46 all of them two If you look at the multiples of this, here you You can write something like this: set d = x is true that x = 2n multiple of x2 is a multiple of x2 Ver ver ver ver n what will happen boss n clear kar Two n Your Belong Does n Your Belong Why does integer become integer because It is positive and it is negative and it is also zero. There are positive and negative numbers, there are zero numbers. also it is there isn't it and and and and and n what is n Your n Your friends n Your look 2 * -3 2 * -2 2 * -1 2 * 0 2 1 2 * 2 2 * 3 then -3 3 can be said to our people n yours n yours -3 or greater and 10 or less It is clear that what I mean to say is just this If I give you something you Should I understand that brother, it is simple x = 2n ok brother means it is a multiple of two where n is your integer, meaning instead of n Now I have to enter integer, so how many integers All of them happen brother, but I have made it clear that You can put n or -3 or th or between them. If you put in ok then -3 then -3 then 2 * -3 6 Now what will be the next integer zero -2 so 2 * -2 -4 next which is -1 then 2 * -1 -2 Which row is next? If you understand the logic this much. I'll give you a message, you'll tell me what your x is. The next one is very easy, so use your brain and set e You've been given a set builder like this. What does roster form mean? Are the elements written separately for you? Well, one, there's a big two underneath it. a big three under him a big four below that a big five below that one Big six and a big one below it, you understand Whatever is written above, its proof is written below. Whatever is written above, its flag is written below. Hey Babua, it was fun brother, it was fun So what will the formula be x is true that x is True, that's something like this x = formula, apply one or then n / n + 1 look up if n then down You have n+1 but need to clear it what age is that n Or you can write it like this: n belongs to Look at the natural numbers and your ones from one to Natural numbers up to 8 are and n is >= 1 And < = 8 I understood it, it's clear boss Now look at it, you will see that x is your natural number. Meaning, instead of n, you have to enter a natural number. But which numbers are 1 and 8 or one and 8 If you put one in the middle, okay, then 1/2 a If you put two, you will get 2/3, if you put 3 So 3/4 will come, see all the elements. If you see it coming then this is your If the answer is clear then the meaning of sets Got his representation roster tabular Property or Set Builder Form now What does MT set mean, very simple. see MT set means MT set means in which MT set means that there is not a single element in it. There should not be a single element for example for Example: A set containing no element at all is called the MT set MT set ko apan log It is also called by some other names such as tap You remember this set, tap set brother, tap set Nothing or void set and this Friends, there are two ways to denote Fa or Then I don't understand anything inside the curly brackets. I came to know that denotation is very important. Friends, we call this sign fi what Let's say phi, okay, this is a Greek letter. it means null set what does it mean Meaning your tap Set void set or MT set empty set mt set empty set okay now a Should I give an example of this, you guys tell me that right here this this this that I'm giving you Let me give you an example first. are like man come on as if I had a set took a I took x is it true that x okay x is true that x is to 2 + 3x It's okay, right? You just look carefully. and and x belong to natural numbers you Tell me what elements mean if I ask you to put this in roster form. What is the meaning of the written roster form? Roster form means that you brother Separate the different elements by comma separation okay so let me write in brackets Tell me what is x brother, what does x mean to you? The set will contain x some elements. Now these x What is x = 2 + 3x then x = 2 + 3x then x What will be the value brother, this is your x there If it goes away then this is 2x 2 and if it comes here then -2 x Friends, you have received -1, now pay attention x You got -1, okay, so you will say that Brother, in set a you will get -1 But there is a problem, he said that x Your natural number should be x. should be a natural number but x then you get -1 Your natural number is not coming I mean what I mean x what is x this is and this is but so It is not possible, right? I mean, these sets If there is no element in here then Friends, will the a set be your fi set or Or you can also just write it like this Karlie Brackett I hope you get the point Isn't it abe bud bracket ch understood brother Clear, okay, so this is your MT set. It happens that there is not a single element in it, okay Now let's talk about single ton set or singlet set. This would be a set as you like it which contains only one element then a set containing only one element is called a single element set for example Guys, suppose I took a set a I Bhaiya said, x is true, that x times x = 2x + 2 Okay, so x is true, so x = 2x + 2, so brother, set a what will become of you, see what I have told you Set builder form is given, roster form what will you write in x what is it brother x yours 2x + 2 is equal to, meaning this x goes over there and it becomes 2x - x x x Your friends -2 So in this set Only one element is coming that I understood Is-2, for example, if I would have given you a set a I told you x is true, that x is - 5x + 6x - 5x + 6 = 0 ok tell me this set Will it be a single ton set or a single ton set? How will he know the quadratic Solve the equation, what is x brother, this is x x If this is there then solve it brother x S - 5x + 6 5x + 6 = 0 You guys know this You can write x s - 2x - 3x + 6 equals 0 So x common x-2 -3 common x-2 equals 0. This is your Boss, let's do it with basic maths, so x - 2 You took the common x - 3 = 0 so x is your 2 3 So you have two values ​​of x, 2 3. Meaning, if you put it in roster form If you write, which ones are in set A? There will be elements brother, there are going to be 2 and 3 Now you understand because it has two elements. What do I say if there are two objects? Bhaiya, I will not call this a single-aton set. because not an object or an element Now here's a very important thing. I'm teaching you to pay attention, okay? Friends, I write like this 2 bings to a Is this correct? Yes, this is correct. Why? Because two is an element, two is an element. that belongs, that belongs, set a belongs to a set belongs to a set if is in a then to belongs sets a to If I write 3 bings to a that's also correct But does fur belong to a correct in this case This is wrong because the four elements is not coming in your set a means four does not belong to your set a then you You can write it like this: Four does not belong to set a you can write it like this okay I remembered a small thing and I told you this I have taught you this thing, let's finish it very easy and Infighting Number of elements in this set and a set that has a lot of If there are elements, then the counting will continue. I will go away infighting her, sorry, let's go. Now here friends, a very important thing you I go cardinal number of set what is the cardinal number of fin it talk about set okay finna it set I will tell you the reason why there is infighting. How many elements are there in the final set? Can you tell me how many elements there are? Friends, I call him Cardinal. Number of sets for example for example I write this as if I had written one by one The set is written as: It has three elements: 1, 2, 3 elements are okay now here's some Learn how to write it like this Yes, can you write it like this also 2 1 3 It doesn't matter, okay, so the order is Not important the first thing you understood Is the order of the elements not the same? I will write it again, what order is Not important order is not important You can write the order in any order. It is not important and remember these two These two are the same thing, these are the same thing Both are the same thing, ok your order It is not important, okay, the other thing Don't do repetition, it's okay, there is no benefit from repetition. It doesn't matter, don't repeat it here. I will write, I don't do repetition, meaning I can't do this, give me an example I will do, don't do What does repetition mean, see and understand it now. It will come, okay, just pay attention, okay for For example, if I had written b a set okay 1 2 1 3 1 2 1 3 okay so a and b a and b are the same thing, okay Hey brother, you write this one twice, what is its meaning I don't understand the sense. One, if you have a Once you have written an element, you have one already. You need to write it a second time. If you don't have it then don't repeat it, do you understand? Gone, now back to cardinal numbers. Meaning friends cardinal numbers mean numbers of elements, how many of your se for example If I ask you the number of elements in The set A is called the cardinal number of a set The meaning of A number of elements in set A Brother, what is the cardinal number of sets? Three because there are three elements in this, understand Here comes your easy and simple talk, let's do one more. Tell me the question quickly, just as I Took one of your B sets as if I had your B set taken okay x is true that x x It's true that X is a letter x is true that x is A letter of goodness, I will tell you this later. I'll teach you this later. I'll tell you, the questions are about to come. Too many questions will not load you Runa ok now Let's do infinitesimals like A B CD etc etc etc. as if I am writing capital A, meaning this is one What is the set of natural numbers? Understand this. I am your infighting Bhaiya set of all integer jars in integer jars Your positive numbers also come Negative numbers also come and your row z+ also means positive integer set of jars okay z minus what does it mean will be the set of negative integers q means What is the set of rational numbers q+ Meaning of the set of positive rational numbers r of real numbers r+ means the set of positive Real numbers, all these are yours. I denote infighting with a capital n z z + q you must have understood the logic now let's go What does equal set mean? what does it mean so it is very easy ok to non Empty sets ok now here non empty means non MT means set your MT Must not be fi set null set void set There should not be any element in it If there are two non-MT sets, Meaning if there is some element in it then a and When will I call B equal when their elements are exactly the same when their The elements should be exactly the same and I I write a ra b for example simple mano I took a set 1 2 3 understood or then like this I took a set 2 3 okay and I took a set x is true that x - 5x + 6 = 0 ok ok you tell me In set A you have two elements t and th If you write Set B in roster form Friends, I just taught in set B. Your two elements will come as 2 3, this means you What do you understand? Same elements in A are also in B. also same elements so here it means What happened is that your a equals also very simple Okay, what's the next topic? What is meant by equivalent set? Bhaiya Equivalent Set Means Cardinal The number of the set will be the same but the elements will be the same What to do to find it sets a and are said to be equivalent to fine I call this set equivalent when Cardinal number of sets A cardinal number of will not necessarily be equal to set B It is okay if the elements are equal, for example For Apple, as if I had set A, set A I took 2 5 6 4 Set B I took 5624 Okay, no, 564 let's adopt this. Brother, give it 1 or 2 10 okay now look at the cardinal number of sets What is the cardinal number of the four elements? How much is the set also four elements so because So because a is equal to a b because sin Since A equals A B is later later for later Four or Four, whether A and B are equivalent Understanding Sets A and B Are Equivalent Sets I came in R Equivalent Equi Valent is clear, it is easy, sure 100% ok Now here's an important thing, equal Sets are always equivalent as many as Equal sets will obviously be equal Sets will always be equivalent but Equivalent sets are not necessarily equal Yes, but the equivalent set is not necessarily be equal such that these two equivalent sets but is not set equal to it, but it could be that you have two equivalent sets It may be that it is equal, okay, so I Hope you understand the meaning of equal equivalent. I'm here now, some quick questions here. Let's do it so that it becomes absolutely clear to you. Set to be converted into roster form The builder form is given in the first one very Easy set a what di ho x is true that x your is a natural number and x is less than 8 then Simple x your natural number smaller than eight so 1 2 3 4 5 6 78 Will it come or not, understand Look, you have converted it into roster form. done whom set a to okay let's second I'm going to do it very easy quickly x is true that x is a prime number x your prime The number which is the divisor of 30 is 30 has many divisors but x What is the prime number that is divisible by 30? Now let's see the prime number which is 30 Divide your set B into Elements come friends one so prime number It doesn't happen, okay, two is a prime number. divides 30 is the prime The number is divisible by 30. Well, f is a prime number divisible by 30. Does it happen? Sen is a prime number But it does not divide 30, it is 11, but 30 is not divided by 15, ok brother It doesn't, let's say 10 does, but 10 prime I don't have a number and there's nothing left, friends. Your elements will come 2 3 5 cardinal numbers The three elements of the set B are Okay brother, what are you saying, set C set S boss what is x x is your integer and between these two or between these two equals means x your 6 less than x your 6 less than and x your greater than -2 or -2 and x If your integer is zero then brother it is -2 or greater than -2 integer then -2 becomes -1 becomes 0 One became two became three became four It's five o'clock, this is your friends' set. The elements have arrived, see, your x is -2 or -2 An integer greater than and less than six is ​​fine Let's do fourth, it's very easy, what do you say? are x is true that x is a two digit Natural number whose digits are even is such a number Read everything in the set builder form Given x is your two digit natural number Now the number is two digits, so many Natural numbers are two digits, boss. The natural number of is even six of its digits So what does it mean that it is in set D? Which of your elements will fall into set D? Friends, look, it is very easy, first two digits Number whose digit is even six Friends will Vanma sorry 15 be absolutely Look, 15 is a two-digit natural number and 1 plus 5 is 6, its reverse friends is 51 It will be done, okay, let's take it now, boss. take it now boss take it now Yours 24 42 and some now take boss your 33 okay It's 42 now, it's 51 now, it's yours Let's take 60, no problem, 60 is also a two digit number. is a natural number and 6 + 0 gives you 6 And what could be, and what could be Boss, can there be anything else, think about it brother. Can anything else happen after 70? Obviously, they will not be younger than 60. I think friends, this is what will happen. your answer It will come, okay, if there is anything else then please think about it. If it's not there, let's go to the next fifth one. Let's do it, okay, so what do you say in the fifth Bhaiya, what is the letter x, what is it x Your letter is Better Word's X is your letter Whose better word is it? So better word is it? Just write the letters separately. If you are talking about E set then B Write down e write down t twice you have here Write it once or twice, you write it once and Come on friends, your set is ready, BTT R, okay what was x letter hai better word ka ok This is the last one, what are you saying, your engine Okay, x is your integer, so let's take this. You leave now Give it to me now, you leave it when I give it to you I'll teach you what linear equations are, then you You can do this question comfortably, okay? Boss to mota moti roster form se set Builder Form Set Roster from Builder Form I have taught you how to do the form. If I were in your place, I would ask this question How do I get that brother set builder form I know how to do the roster form but The Set Builder form is slightly different from the Roster form. If it seems difficult then here I will concentrate I would have given that if I had been given something like this then I I can write it like this if I give it something like this If I were, I could write it as if If Set C had given me something like this, I would have given him I can write this in the set builder form Suppose if set D had been given something like this then I We can write it in set builder form like this I feel like if I had been given something like this, I I can write to him like this, did you understand? If I were your world, I would Let's keep going, boss, let's go to the next one now This this this this is very nice what are you saying These are basic questions, let's move on to the next one. We will move forward slowly and complete everything. I will get it done, everyone please pay attention Speaking of writing in the Mantai roster form Good roster form Meaning, the elements have to be taken out and written separately. in curly brackets okay so set a what He is saying that brother, the set is A, what is your A? Bhaiya this is a good set, you have this there I deleted the second question. Because it was of no use, it is true that What is Boss n your natural number to belong Does n belong to your natural number? It does and you've got A+1 for your is equal to 3an where a1 gives you One is given, well something like this is given Now understand my point, who are there in your set Which elements are in your set? There are elements, let's talk about them first. Set friends A A A elements means this is a It will be written in your set but pay attention a means n your natural number means a1 written It would be a2, it would be written a3, a4, a5, and you get it. This is your infinite number because natural numbers are never It won't end, now I'll take it out All the elements are in a1 so I already know This is one, a2, how do I find it friends? From this formula, you can find a2. Okay, so let's focus on finding a2. to extract two a2 to extract a2 You have to replace n with one, is that logical? Brother, to find out a2, replace n with v, so if If I replace n with v, this is your a1 form. 1 3 a1 so this is how much your a2 is your a2 31 means 3 * 1 so a2 is yours 3 a2 is yours 3 Take it easy and watch it now if I n I put oo in place of If I put u in place of n then this is your a 2 ≡ 1 ok a2 + 1 = 3 a2 instead of n If I put 2 then a2 p a3 3 a2 gives 3 yours. If it has come then 3 3 9 then a3 9 here we go let's see another one next a4 a4 How to extract it, if you do it then extract A4 What you need to do is replace n with 3 If you replace n with th, you will have to keep it. replace a3 with 3 so see a3 1 a3 1 = 3 a3 So this is your a4 3 a3 means a3 is your neither a4 Your friends, 27 have come, okay, how many such If you want to take it out, then four times three times four also The work is done, just write it down and that's it. What is the answer, what is the answer, Karli bracket curly bucket a1 means and a2 means 3 3 means no after that 27 dot dot dot dot Put a dot to show that Brother Infino has brought such questions for you. Your concept is also very good. What are you saying brother that you have developed from Fa is and this is inside the curly bracket Some zeros and zeros, all three different Are these three different? Think and see. Yes, this is different, let me tell you about O-Fi. Meaning Fa means MT set means one here There is no element of Fa, meaning this is your MT is set okay what does that mean Something written inside curly brackets is curly Something is written inside the brackets, meaning this is MT If it is not set then these two are different. Boss, this is an MT set, this is not an MT set. Because there is an element in it, your friends It is a singlet set, you can call it a single ton set. You're okay and zero and what is this boss this So it's not even set, it's not even set Not a set, not a set, so all three are different. That it did not happen, this is not a set, this is a set which contains one element and is the set containing Not a single element Void set MT set Tap Set Next. Some more questions, what can you say? You have been given a roster form in if n now pay attention x a set you What did you say is given in the roster form? If n represents any number of x What are you saying and what do you represent? What does x represent? does any number of x mean any number of n The value can be anything like 1, 2, 3, 4, 5, 6 Express the following edge sets express the Following edge sets we can call them as sets If I have to write then I write the first one first what are you saying n does it belong to you x what are you saying to n that is your x Belongs means he belongs to x It means it is either one or two or three It will be either four or five or six but butt butt 2 * n does not belong to x means butt 2 * n does not belong to x understand its meaning I'll tell you, as if you had took one, okay, so the value of n becomes one Okay, so what will be the value of 2n? I understood that the value of will be 2 but the value of 2n Two is coming, she is also a part of your set. I will say it again, that too from your set There is a part but what are those people saying that 2n should not be part of your set I did not understand, Guruji, look at the value of n My love, anything can happen 1 2 3 4 5 6 okay but on you on you which of n will take values, will take those values ​​for which 2 * n your set ka part na ho aaye for Example: If I take n as 2 then multiply by 2n what will be the value of 2n if the value is four Now the value of n will go to what you want your set to be I will include you or not, why? Because the value of 2n that is coming out to be four is part of your set is what n = 3 if you If you get 2n then what will you do? Will you include it in your set or not? Because the value of 2n is your set But if you pay attention, the value of n is 4 So the value of 2n is 8, the value of n is 5, so the value of 2n is The value of n is 10, the value of n is 6, so the value of 2n is 12 Okay, now if you look here, this For values ​​of 3n which is the value of 2n 8 10 and 12 are not part of your set 8 10 12 If it is not part of your set Just by taking these three values ​​you can set your own Make it, if you understand then what will happen to your set Bhaiya, yours has become 4, 5, 6, why? Because these are the elements of x that have In which if you make 2n two to these Multiply it, it's not part of your set Okay, let's go to the next one, sorry. Boss is saying n+5 should be your 8 So brother, this is a linear equation of n. The value that satisfies n + 5 = 8 so 5 went over there 3 the value of n is 3 what your If it is part of the set, then yes it is yours. Friends, the B set will become like the single ton The set is fine, let's do the third one, what do you say? are boss n is greater than 4 n is greater then 4 so these are the six values ​​of n out of which Which is greater than four, only F and C As if Set C became yours with 5 and 6 Easy, I think it is very easy, let's go next What are many saying next? Excellent Question y your this means y set is from one What is a doing with natural numbers up to 10? Yes brother, it represents any element of y a what is your represents Any element of y means the value of a 1 2 3 4 5 6 7 8 9 10 It could be anything Okay, right, the following are set similar. The question is to write them as a set. what are you saying boss, what is the first one Boss is saying read that a to your y should belong to a certain should not belong, okay look at one The value of a if I take one squared of 1 one hota hai does he belong to y If I am doing this then I will not take this to you. If I take it in one place then 2 of 4 is that y If it belongs to someone, it also belongs to someone. I won't if I replace a with a three. If I replace a with th, then 3 s 9 vo Bhai Nai will also belong to you here will come but if I replace a with fur then it will be 4 S 16 He doesn't belong to you You guys understood that yours is like a capital A set will be made, what will it be brother? Bhaiya, it will be made and you will have five points in it. It will be six, it will be seven, it will be eight, it will be nine and 10 Why did you take these seven values? Because if you square these, they will Does not belong to y 4 5 6 7 8 9 10 OK Let's go for the second one, what are you saying boss? a + 1 your 6 a belongs to your y So a has 10 values ​​a + 1 = 6 means a = 5 so b set friends your five will become Okay, what is the third one saying, boss? is less than 6 and a below to y so this is your Les Dan is 6 and belongs to y Meaning 1 2 3 4 5 of yours will fit in it. Easy, let's go, next topic is very important. Now the interesting things of the chapter start Getting to know what subsets mean Boss subsets what does Boss mean pay attention ok Let a and b be two sets if every element of a is present in b so I I say that a is a subset of b for Example: I took a set of 1 2 3 4 pay attention okay as if I had a set took 2 3 okay obviously both na Is this equivalent or is it equal to me? I am slowly understanding these things. You will keep thinking that it is neither a single letter nor an MT. ok it is getting clear, it is getting revised I will keep talking in between, okay now concentrate give okay friends what every element of a is present in b means that whatever is in a set elements that are in b are also in a set Are the elements present in I also present in B? is a set has two is three is and two and th b If I am also there then what will you say that a is a subset of b a is a kya bologe boss a EA is a subset of B and how to write it If A is a subset of B, then it is called represent the understood subset I understood it, okay, now just listen. Listen to the story, now believe it, believe it, if I took a set of C I took a set of C Elements of your TV 34 Dhyana Tou Answer Karo Kya C B is a subset of B if C is a subset of B I want to ask you a question, boss, what is the question? Hey boss, pay attention that is C is C set Specify the subset of B. How will the question mark indicate if C All elements of B are present in C if All the elements are in B, look at the fun in 3B coming in fur b coming in to b one is coming in b then all the elements b is present in means you Can you write in simple language that c is also a subset of b so what you write c is a is a subset of b, I understand this correctly. and and and keep watching just think okay I took the D set, I said one, Said one, you understood friends, the d set is also yours b is a subset of d because the set contains elements in all of your b sets If I ask you, as if I bought an e set and told him brother I told him brother what did he say 1 2 4 2 4 Can I say that even the set is a subset of b can you say those Why is it that e has as many elements as One, two and four, that exists in your understanding. I'm here, okay, let's see another one. Last Mano Mano Mano I took f set I said 1 5 and 6 1 5 and 6 what f your is a subset of B so one occurring in B is 5 I am not coming to B 6s I am not coming to B So what you would simply write is f is not a subset of b You can write it like this f is not a subset of b you can write it like this Understood the meaning of subset if a of your b is a subset means all the elements of a are in your b will be present in Now here is a very important thing for you. It comes, pay attention, pay attention, how many What are the subsets of any set? I told you how many subsets, you should note this. By the way, note down everything has to be done, how I'm talking about many subsets. anyone that anyone and you also have a formula I will tell you that brother, whatever set it is, how much more than that are subsets, then for example, for For example, I gave you questions one by one. The set is 1 2 3 question will come such that right All subsets of a kya bola right all subsets of a as many subsets of a as possible There are as many subsets of a as possible. Write it all down and show me how I will write it. Okay, so let's say I've set b I took it and said One is fine or you can write it like this, one one set It will be okay Well, to be a set, there will be a set. Friends, whatever this set will be, it will be a subset of this which is this set is a subset of this It is a set, it is a subset of it, brother, you understand. Suppose I called it a D subset, so what? is a subset of is yes because which in D element that exists in a logical understanding If you go, then these three sets will be made, what else will be made can friends take 1 2 t also subset Its friends will take 2 3 2 3 also subset It will be okay guys 1 3 take 3 1 1 3 The set is the same thing, no matter the order It doesn't matter and what will happen to him now? pay attention he himself is fine okay means every A set is a subset of itself and one more thing The phi set is also a subset of the mt set is always a subset of every set, remember this The question is how many subsets you have come to count? You will see there will be eight in total, how many ek doti cha pa 6 to 8 Now from here I will tell you a formula I'm your number one on any set If we remove the subsets then the number of subsets There is a formula, note down the number of The formula for subsets is 2 to the power of n What is 2 to the power of a where this is n this is your number of elements what is it Number of Understand the elements, understand the logic, sure of the logic Okay, mark it with a star. Very easy, now the answer to one of my questions give believe believe believe believe believe believe As if I asked you a question, I have a b is a set such that n b is a set f which means that b is a set There are five elements in the set b There are five elements in it, their number How many subsets will be formed? Number of subsets Tell me brother, suppose there is a B set in which Write the elements 2 3 4 5 6 five elements How many total subsets are written? The number of subsets formed is equal to the power of two If there are 32 elements then 32 subsets will be formed. I've got 32 subsets, okay, one remember the thing Keep in mind that every set is a subset of itself. Every set is a subset of itself and is also a set of is a subset of this, this is what you wrote here What happened was every set is a subset of it The MT set itself is a subset of every set These are the two things I taught you. Every set is a subset of itself, meaning a a will always be a subset of b will always be a subset of b d will always be a subset of d and mt That is, the Fa set is a subset of every set. Meaning, Fi is your a's as well as b's as well c's as well d's and every set has a subset phi of phi. At last it is written the total number of sets of a finite set containing n elements is 2 to the power n if any set If a has n elements then how many subsets does it have? I will make you Power A subsets. I have already told you, okay, just okay sir Okay, here's another important one. Let's talk about proper subset here, brother. What does proper subsets mean? what does proper subset mean okay let's I will explain later what proper subset means. It is proper to listen very carefully subset okay proper subset means if Let's say I took a set of 3, okay, how many? How many subsets will be formed in total? Do you know that total subsets will be formed from this? Power a means power aa subsets of u will be formed Okay, write down which ones they will be from and why. F will be one, O will be three in the set will be t will be 2 3 and 1 will be 3 or you can also write 31 be and what else and 1 2 3 would be okay so one Doti cha pa 6 sa aa these are your eight subsets But notice one thing here very carefully. Do if I ask you to do proper subsets Tell me what one said if I ask you Proper subsets of a I will understand only these sets further. These are your proper subsets, got it? Your proper subsets Remember proper subsets are proper subsets. In a set which is a subset of itself I don't understand, I understand. It has come in proper subsets which always There will be elements that will be less than that set Brother, there are three elements here that are equal to It will not happen, okay, now how to denote this Let's do it for example for example Friends, let's denote it like this: ff is a proper subset of a proper subset in You don't put the equal sign below, you can understand it like this Can you tell me when I will put equal when these two When I include this too brother, this It is equal to this, isn't it, it is equal to this, understand? I came, well, what else do you think I should write? One set is a subset of a The two sets are proper subsets of a. Okay, three sets are proper subsets. is a set of a that is a proper subset of a Similarly, the set is proper. is a subset of A okay and then you're done And your 2 3 2 3 is your proper subset of A. Okay, and if ta 1 2 3 then this subset so is not a proper subset of, so here you write like this I understood, I understood brother, it is definitely clear. 100% ok Guruji so if I ask you I ask you, please pay attention, please pay attention, okay It's as if I have a set I've told you Ask me if I have a set that is a cardinal number is a cardinal number Suppose set A Of 10 ok How many proper subsets will there be? Number of Tell me the proper subsets, apply your mind to the number of Proper subsets are asking for the number of How many proper subsets There will be number of How many proper subsets will there be? How many subsets? There will be power of all the elements If you put it in, 2 to the power of 10 means your 1024 Reduce one, which one am I reducing? Which one am I reducing into subsets? There is also an equal set, I am less in that. I'm doing it, okay, so just 2 to the power of 10. -1 friends if 1023 comes then so proper Subsets will be formed of the set which has 10 If there are elements then you guys understand the formula The formula for proper subset is here I'll write down the proper subset of The formula is the number of proper Proper The subset formula is 2 to the power of n and Subtract one ma from it, note it down. It's easy to understand brother, ok Guruji Let's go ahead and see how you see this You have asked a question, what are you saying? In the question to find it sets have m and n elements then two finna it sets is two Fine it sets means limited in it If the number of elements is then how many elements Yes brother, one has m elements and the other has What are your n elements understanding? Okay brother, what are you saying now? The total number of sets of the first set is 56 more than the total number of subsets of the Second set relax before I tell you I have a question about subsets. So tell me if a set is A if a set How many elements are there in A? elements if there is a set B in it How many elements are there, n elements means Suppose there are 10 elements in this, 11 in this The elements can be anything, tell me. What will be the number of subsets formed? What is the number of subsets formed by a of a What will be the number of subsets and the number of b How many subsets will there be, brother m There are elements, whatever number of elements there are, So put it to the power of 2 a set of m will be subsets of the set B to the power of 2 n If there are subsets then you will understand the logic. Now what are you saying in the question? The total number of subsets of which subsets of the First Set Well, the first set has m elements in it. The number of subsets is 56 more than the total what is the number of subsets of the second set There are seconds in the set of a few seconds in the set Some subsets will be some of the first set There will be as many subsets as there are in the first set. There are 56 more subsets than the other set Do you understand the meaning of subset? Do you understand the point? Like for example, suppose I set A I said like I said 100 elements 100 No. Assuming how many subsets of set A are there? 100 sets of B are being made, your 44 brothers are being made. Got it, now tell me how much more than 44 How much more than 100 44 is 100 56? Do you understand how many subsets of B there are? How many subsets does 100 have? has more subsets 56 has more subsets So he is speaking to himself in the question. that all the subsets of the first set are What is it brother, that is 56 more than the other set The number of subsets of gives you this equation It has happened and I told you that the values ​​of m and n First find out if you understood the logic brother. This is the number of subsets of a set, which is 56. Is too much in the sense of the number of subsets of the second B set How will you solve it, see how your mind works. applied 2 to the power m - 2 to the power n together Now write to me how to solve this. I don't understand anything, I understand so much that If you can brake 56, then brake 56. I did it on 56 by breaking my friends can be written as 7 * 8 means 7 * 2 to the power of 3 That's right, I wrote it here brother 2 to the power of 3 * 7 no problem no problem So your 2 to the power n to the power of 2 n is now in the power of 2 or the power of 2 If I am not there then what did I think? 3 to the power m - 2 to the power n 2 to the power and Friends, I wrote this down. wrote into 2 to the power 3 - 1 can we I can write 7 like this: 2 to the power 3 - 1 Brother, 2 to the power of 3 is 8 -1. Okay, now let's move on. Solving this gives 2 to the power m - 2 power n = 2 to the power 3 going into it 2 to the power of 3 going in and this is 2 to the power of 3 * 2 to the power of 3 will give 2 to the power of 6 Power 3 * 1 so you get 2 to the power of 3 Now compare something like this, now compare it. So m your friends 6s have come n your three a okay so how many in the first set There are elements brother, there are six elements, so How many subsets will be formed to the power of 2 to the power of 2 6 subsets will be formed in the second set of your n i.e. There are three elements, so the subset of your two Power th will become 2 to power 6 means Hey friends, 64 means 2 to the power of 3. How much more than 8 8 is 64 56 more then the first set will have 64 subsets of the second The set will have eight subsets of the first set How many subsets are more? Understand how many 56 are more. It went easy, I think it was very easy, let's move ahead. Let's move on to the next topic. But one small thing is something to understand. Pay attention, okay, friend, intervals age subsets of r okay now first you have a Let me tell you something, is everyone understanding this? Is everyone understanding this, brother? that natural numbers are a subset of whole numbers Whole Number Is a Proper Subset or Subset of subset of your z integer jars z integer Jars is a subs of your q rational number and Is this your real number? Does everyone understand this? It is a very important thing to notice Wali Think about it, what does it mean that natural number is a subset of whole number because any number Natural numbers are all wholes numbers means sets of this whole number I will have all the natural numbers. You will understand that rational number is a Subset of real numbers into real numbers Are all the elements of your rational number They will be included, they will be because All the elements here are here All the numbers here are here so this is a subset of this then is a proper subset of this I have come, okay brother, okay, okay, okay. Now try to understand here or What does closed interval mean? carefully close interval of ok as if If I wrote friends, if I wrote like this what I write if 1 2 it means What if I wrote curly brackets 1 2 If I write curly brackets 1 2 Meaning there are only two numbers here. There are two elements one and two but if we assume I wrote this, if I had told you this bracketed Meaning of this bracket It so happens that there is one and two here, but The number of numbers between one and two You know there are a lot of numbers. Infa me numbers are all those numbers too I am sure this is what I understand Your closed interval is said to be closed. Meaning one and two are included and between them All the numbers are there too, do you understand? I you can also write it like this and and that x Suppose x is any number, which number is it? Bhaiya x your one or one is bigger than two or two I understood it a little, it became clear, this one That's it, you should know how to write it, okay? For example, if I write 2 4, it means What if I put a close bracket? So that there is 2 and 4 but in between them There are a lot of numbers, I understand. Brother, now what does open interval mean? Open interval means on bracket as if I had written 1 2 like if I What does this bracketed sign mean? One and two are not included but between them All the numbers are there in it, it means okay If I write this, it means one and two. All the numbers between I am talking about it, okay, so you And you can also write it like this that x x means Which number is bigger than one and smaller than two? It's clear, boss, it's clear, so it's close. Interval this is your open interval, this is your Sometimes you also write it like this or you can write it like this Meaning, put the opposite of this, close, okay. It is also written like this, okay, it also means the same thing. that I am not counting one and two, one and two I'm counting all the numbers between cm What does it mean to close or semi-open? It means half close, half open, something like that It's like I wrote this here. Closed it here or else It felt like what does it mean is something such that x The number that will be one or greater than one and two Smaller than means it will not be two, understand what? I am getting clear what this means That brother, there is one, everything between one and two The numbers are also clear, it is okay. You can also write it like this: there is one and two No It is clear brother, so these are the basic things for you. You should know, now look at the universal set. What is meant by a set that is given? Understanding that all sets are subsets in context is not a subset of what is given All the sets in the context are The subset is I will say it again I will say it again ok, I said the wrong thing, okay Again the universal set let you Let me tell you by example, suppose I have a set taken tooth fur dot dot dot d up to 10 okay up to 10 I have taken your natural numbers as if I took B a set 2 4 I took C a set taken 3 I took a set from T5 okay and Suppose I took a set of 1, 7, 8, 10, and 2 Okay, now understand that I have a Set the context and enter a contest. It is a question, in a way it is a question, okay In this question, all these sets are Is it a subset or not, is it all a set? Is it a subset of this or not, meaning it is as many as All the elements are present here. Friends, what should I say to this person who what this is is the universal set what this is It is a universal set because it is compatible with all these Containing sets is a given understood in context It's clear, okay Guruji, it's fine now. You will gradually understand this. For example, believe me, you are good, it is not necessary That this is a universal set, isn't it? The set is not unique as if brother is in the same place Suppose I wrote b a set b not suppose I wrote f a set from one to all Natural numbers up to 20 are fine, so are these. Also, the universal set will be understandable for them. Okay, here comes a set that covers everything. Elements Contain That Given Context I am clear, okay brother, now it is good. Here are some words that mean superset: I mean, maybe I didn't tell you. I had forgotten this, let me tell you now. Look like you know that b is a subset of a ok b is a subset of a c is also a subset of d of A is also a subset of A and e is also your is a subset of A I understand e is also your is a subset of A okay now understand B is your a is a subset of you can also say that a Is it a superset of your B? Write that A is your B's if I believe this If I wrote it like this, it means a It is a superset of your B. Understood, B is A. subset of a is a superset of bb is a subset of a a is a superset of b what I understand, okay boss, let's go now. Important, that was such a stupid thing. What is the meaning of power set, very easy power set like I took a set okay I took the basics, the basics, 1 2 3, okay. If someone asks you, that is, the power set of a Tell me who asked you what, brother? Power set of a, what does it mean? is a simple power set, meaning there will be a set Power set means there will be a set, power set Meaning there will be a set whose set is the set of all The set of all subsets is called power. Please note down the definition here. Whose set is this brother, set of all The set of all subsets is called power. Set a Guruji, give me an example and understand from that. I know nothing like this, brother. Similarly, class 11th maths is very difficult. There are so many things in one chapter. It's easy, don't worry, okay, man. I took a set 1 2 3 which of its subsets will be from, will be fa, will be curly bracket and will be curly bracket to hoga curly bracket th Write all of them in curly bracket 1 2 will be curly bracket 23 will be curly Bracket 3 3 33 will be yes or write 3 There's only one thing and one is your T3 you know There will be eight subsets, listen to all these now. The interesting thing is all these subsets is a set of subsets if Let me make a set, this is called a power set of a power set means this is also a set, this too A set is a set of which subsets mean Which elements are in this set? I understood whose subsets were cleared. Now, just tell me one thing here. two pay attention okay the question is as if a Or let us assume that A B means cardinal number. Offset B as if it had five elements, four element tell me its answer by thinking quickly Guruji, I don't understand the meaning of this. Answer How will you tell Cardinal number of power set of b means Power set which will become brother of B in B set There are four elements in the set B. How many elements are there in its power set? You will be asked for the elements How will you tell me brother if there are four in set B If there are elements then power set means what is B's Make a set of all the subsets. The set of all subsets of B If you make it then how many subsets will Bhaiya B have? 2 to the power of 4 will be 16 subsets and that's 16 Make a set of subsets so friends power Set B will also have 16 elements. If you understand then it is simple, you will understand from here. There are as many subsets as there are numbers. The power set contains elements. If I come then you write the number here Elements Number of elements in power set Power The set number of elements in the power set is Equal to number of subsets is equal to the number of subsets, simple thing Brother what is power set Brother what is power set is the power set of all subsets The collection will have as many subsets as there are Elements will be in the power set I hope you The matter is clear now, there is a lot of The best questioners I hope you are enjoying it, stay tuned. Brother, let's move ahead, let's base it on this. Friends, let us look at some questions that power How do the questions come on the set? It's very easy. Yes brother, it is very easy, but from here you There will be a lot of interesting things to see. You have to, right, if a equals something like this given Have a look at the set carefully to understand it first. Try what a set has given you. Curly brackets mean set and in it Which elements should you focus on carefully? One element is a and one element is curly Is this bracket B? Do you understand? There are two elements here, one The element is a and an element is a curly bracket B. Do you understand this and these A set is created with both elements. Now, did you understand something here? I will ask basic questions brother, please pay attention If I say that your a belongs here let's write this a okay if I should say your a belongs to capital A. So is this True or False? Yes, please answer, this is true, why brother, a one element is element belongs sets a is doing yes if I write like this b bings to a is it right b belang to a How to check if b element belongs to a set belongs to the brother b element in the set a It is not there Guruji, it is not visible. This element is not b, this is curly bracket b I understand this is wrong this is wrong this is right Pay attention if I ask you one more question. that curly brackets belong to a set If it does, it's perfect because Element Belongs to Set A Now Focus tell me true or false okay if I write, if I write, brother. So, okay, pay attention to the curly bracket b. subset of a that is true or false Things are getting interesting, think about it. what I wrote curly bracket b is a subset a of is this correct you will say you You will say, brother, you understand the subset, right? curly bracket b is a subset of a, this is wrong bud bracket b is an element of a is an element of It is not a subset but an element, you understand me. What am I talking about here is the subset The sign will not come, the key is not set. Friends, if this happens, see Curly Brackets are also elements, curly brackets are also elements If the element has a set sign Given this subset of a it is correctly written It's a strange thing, but remember the set. This element in the sign element is Karli Brackets are also fine, well I have told you this. Told extra things and knowledge You will be asked a lot of questions about this. A set is given that contains two elements I told you to take out the power set of a First of all what I will write is subsets So the first subset will be F, okay? The second subset will be whatever element is there Pick up and bracket whatever element it is. Pick up whatever element is there and do it Put brackets, did you understand? Yes Guruji, and If you take these two together, you took a took the curly bracket b and made its set So friends, you know there are two elements. So 2 to the power of 2 will become four subsets. Subsets are coming and the power set of a means What happened to whatever subsets you have? I have made the set, I will say it again 1 2 3 4 These are subsets, you have created a set of them, understood? So this is your power set of A, it has become clear. Happened 100% Guruji, I am understanding it quickly. We will answer basic questions quickly. No, this will make you stronger friends. What are the concepts saying before relaxing? Look at the question, understand what one is saying. It is a set, it contains one element. There is two and there is an element 3 4 that too curly What do you understand in brackets 3 4 is an element in curly brackets then you Do you understand that one element is one element? Two is one element, this is the complete bud bracket 3 4 This is a complete element, you should understand it like this set inside set inside set then which The inner set is that element, what's the matter I understand that there is a set within a set. is set inside so the set inside is now set No, it's an element, okay, and this is one of your Element five is now what's in the question said part of the following statements Incorrect and why, let's keep it simple Bracket 3 4 subset of a is true or Falls, is this true or false friends, bud Bucket 3 4 Element Hai Element Always Belong Does not subset brother if I Write whether u is a subset of a subset a of n 2 is an element such that a If it belongs to a part of 2a is not a subset of a sibling subset of It is necessary to have a set here, understood? Very good, Guruji, look the set is ready. Friends, this element is complete if set in it If you had felt it, things would have been different, then this is your False Done Watch Now Curly Bracket 3 4 It belongs to A, so brother, this is the element If it belongs to a then it is your truth Okay, 3 4 curly brackets, so look at the element. The sign of the set in the taken element separately I applied it brother, this is your element, this is yours If there is an element in it, then it is set, now Your subset will be a of is true okay one billang karta hai ko so 1 a is coming in True is one subset of a It is false Understood Brother, this is not a set, so how can it be a subset? which is not a set will be a subset of the set No, that is not a subset, okay Babua, I will make a bracket. 1 2 5 subset of a so one is an element to is an element phi is an element If a set of elements is created then it is obvious that That will be a subset of a, so this is true for you. Got it 1 2 F belongs to wrong Friends, Natu ka Belong means element hna. If I want it, is it the entire element? Then look at the whole meaning of belong, this one here It is written that this should be your element. Should be an element Is this an element? Guruji, I am not able to see the curly brackets 1 2 f Do you understand where this element is visible? Brother, this entire element should be there, meaning this This whole thing should have been included in the set. your false is okay curly bracket 1 2 3 This is wrong for subset A, why brother, there is someone There is no element here, so there is no If Guruji is there then no no no no No, there are only four elements, Natu Curly Bucket 3 4 and f are four elements here our There are no three elements friends, falls It belongs to an interesting set of If f is a set, it can also have elements It could be an element as well, but here Where are you looking at Fai, meaning of brother belong The meaning of Belong is that element Should this be an element? If it is coming in or not then it is a fall. Given that every set has a subset that is true Bracket F is a subset of a curly bracket F is a subset of a. This is true or false if There would be an element F if there were an element If you put the sign of a set on it, it becomes a subset. Fa is not an element, so this is your It fell, I understood this basic thing now. I will ask you one more such question to take tension. Never mind, let's try this one once. Yes, it has become ours, friends. You delete it, very good, come to this. We will quickly ask similar questions, now look at one. Element fa is an element curly bracket Fa is an element One is an element Curly Bracket 1 is f and one element is two, remember Keep the sign of Belong To if there is an element If the set is there then the sign of the subset will come Okay, so f belongs to a, so what? This is an element, yes this is an element. This is your true curly bracket. What does a curly bracket f a element is yes curly bracket f one If it is an element then this also becomes true for you, okay? If the curly bracket one belongs then curly bracket one curly bracket friends One is coming no no no no what brother if This is the sign of Belong To, meaning this element There must be a curly bracket here The forest is not here, the forest is here, so it is yours False OK Curly Bracket 2 F If it is a subset then brother, if you say subset then remember Put u and f this should be your element Is there a two element? Is there a four element? Yes. So I took both of them and put the set sign on them. This is your truth, okay, Subset said this It is not set at all, it is not set at all This is false, okay, very easy, good This means not a subset. Okay, so two is an element, yes two. One element is curly bracket one element is curly bracket one element There is no one element, the curly bracket If there is no one element then brother, this is wrong. It is not, it is not, this is wrong and its set is made up of is not a subset of a this is true Bhaiya why is it true because yes bhaiya this is not a subset of okay well now here Look here, the curly bracket two is right here. No, there is no curly bracket to element. There are no curly brackets or even elements. It is here, so you can see it as it is. If he is giving then this also becomes true. Why did he write 'not a subset'? Isn't it five, now I have said subset here. Look at the subset, say, then first look at the fa What is the element? Yes, it is curly bracket f. is an element of yes is curly bracket and of If it is an element, yes it is, then it is also an element. This is also an element, this is also an element If a set of elements is created then this will be the subset Yours is really interesting to note. Now subset said so here it is set Now let's look at the curly bracket f element is curly bracket fa an element and put the set sign in it, then Subset Became True I have understood, it is clear boss, okay Guruji. It's clear, let's see it now brother, it's interesting. This one is a very good question. Very good question, I understood it. Okay, so brother, set A is given to you like this. I asked you to find the power set of A. What did I say, how many in the power set There will be elements, one element is F, pay attention Write this first, pay attention brother, pay attention Diyo Bhaiya, there is an element Fa, there is an element The curly bracket is fa and its set is made So there are two elements, so the total number of subsets is How many 2 to the power of 2 are four subsets? So the first subset will be Fa Fa is a subset of every set then this Raised element and installed gusset bracket element and place it in a curly bracket and then these two elements Fa picked up the curly bracket fa and put it in If we put the sign of the set then a subset is a subset this a subset this a subset this and If you make a set of subsets, then it is yours It is called the power set of a, see who it is brother The correct answer is Fa Karli Bracket Fa Karli curly bracket f and look here look here a a Meaning of a means look at this whole thing This is your A, this is your A, understand? If you go then your option number C is the correct one. Answer friends Okay, I understand for sure, okay Guruji. Let's go good It's a good question, please pay close attention. Your concepts are improving NCERT In this lecture you will go many times above I will provide everything if you have patience. If you look at it carefully, you will understand everything. something will be made okay how many elements does How many elements will the power set of a have? in the power set of A if A is your f Things are getting weird but it's easy to see Hey guys A5 means a set which is MT There is a set which is MT. How many MT sets are there? Elements in it, number of elements e How much has it become, brother, even one MT set Element is not MT set even a single element No, yes, if it were like that, there would be a element fi hota sign of set one element It would have been fi but this a said fa to you a said fi to you Bola means number of elements i.e. your If it is zero then what will be the number of subsets, boss? What is the easiest number of subsets to be the Boss number? of subset 2 to the power n a means number of If the number of elements is zero then 2 to the power of 0 will be the same subset, meaning it has a There will be only one subset and which one will it be friends will be a subset of this will be a subset of this That would be only a subset of it I will only understand, I understand, now what? How many elements are there in the power set of A? It will be good friends, as many subsets as there are now So what will be the power set of a if the subset If it is Fa then make it a set of any subset. If we go then how many elements are there in the power set You have one element in the power set correct. then the number of elements in the power set of a Your One Number of Elements in Power Set of a your one a I understand now that such a wonderful thing Very very very very wonderful question What Number of elements in power set of power The set of power sets of four will be this proof How will we do this, brother? Sir, we are I started scratching and I couldn't understand anything. We will do it slowly, okay friends, look at it. there's a set okay I just told you Let f be a set such that f is okay which is fa means you get the power set of a Power set off has to be removed, okay, so power How will the set of F be determined, it is very easy, I mean How many elements are there in the power set of f? I'll figure it out, just pay attention. rest easy okay let us know if a There is not a single element in it f then number of I just told you the number of subsets subsets will make your 2 to the power 0 the same A subset will be created and which one will be yours. It will be F, so brother, power set means subset here But I'll write down the last question. subset your f is done then power set of A will become whatever subset is If you make a set of it, then one element F is coming in the power set then the number of elements in Power set of a your coming one number off Elements in power set of a your coming One now the power set of power set of f means Its power set also has to be made, this means its This power set also has a power set How many elements will be there in it? We need to know the elements. I mean friends, there is an element in it There is an element brother, consider it as a set Treat it as if it were a b set in the b set is an element and b is an element in the set How many subsets will be formed? 2 to the power of 1 If two subsets are formed then the number How much will the power set be? Two power sets Yes or no, I can say that Number of which implies number of elements In power set of powers at of a your to a Now you understand what will happen, now you understand this. Now you treat it as a set brother, this set It is the same, suppose you have set it c c set has two elements in C. The set has two There are elements in the set that you have two elements okay so c in the set if two If there are elements then what is the number of subsets 2 to the power of 2, that's four subsets. Four subsets will form four power sets. I got it, it's great, so what else is there here? Brother, you have to write this employee's number of Elements in power set of power set of Power set of a or f then tell me how much a Four will go, four will come, did you understand? what is made what is made what is made what happens, what happens, matter I didn't understand it, I understood it once again. Try to understand, think and understand everything will come okay and absolutely anytime anyone It is a long session, isn't it? Lack of motivation, that I am not able to make friends You will go in the middle, see if this Your lecture is for three to four hours. something or the other, nothing or nothing, a lot to you The fellow must have gone after studying and seen with his eyes You will understand from me or the guy's wife. I was wondering if he was teaching the genitals or just like that. I have come, okay, I have come for you. I will definitely give you a perfect one shot I will not lie, I have to complete the lecture. Yes, do it in installments, what does installments mean? what about brother one hour then one hour time again I say, complete it in one hour. I am staying in between so that nothing becomes so big Lecture is 100% things but also things on 70 If you understand at once, this is your It's a win at 30, but you can see it when you look back. ok ok what are you saying in the question X is a set like this, oh brother, or a set It is like this, O brother, then prove that this is a subset of y is to prove that a subset of y A subset means all the elements of a set. All of them will be present in Y, brother. If X is a subset of the means of X All the elements that you have will be yours. will be present in y well okay so most First look at the set builder form, not good If it seems then extracting the roster form equals x Okay guys, n is your natural number. is your natural number and it gives you some If the formula is given then let's work it out brother Let the value of n if I put 1 then 8^1 - 7 * 1 How much did you get brother? 8 - 7 1 1 - 1 Your friends, zero has come a lot Well, if you put 2 in, you get 8 s - 7 * 2 - 1 is 8 s 64 64 - 14 50 -1 49 Awesome, see you next if you n = Put 3 then cube of 88 - 7 * 3 -1 then cube of 8 Cube your 512 - 512 - 21 so 1 11 to 2 Gaya 9 491 490 is coming guys this is right this Your 490 is coming, is this 490 correct? Well if you put n = 4 then 8 to the power is 4 Whatever comes will be seen roughly in x Your look If you keep adding finite numbers, you will keep adding answers. If it keeps coming then 0 49 490 dot dot dot Let's see, something like this is coming okay let's see y now so y if If I replace these with forests, then this will be your result. will go 49 1 - 1 so you have zero, if you n then put t in place of 49 2 - 1 Dos 49 came very good if If I replace n with 3, 49 3 - 1 So there you have it friends 3 - 1 2 49 * 2 your 98 this is your 98 if If I replace n with 4, this is your 49 4 - 1 So 49 * 3 will be yours, 196, you try it. Can you 190 No no 49 * 3 will give 147 What 147 okay, just keep doing it like this If you go, you will understand roughly. Is that your first element? Zero then 49 then 98 then 147 and so on will go will go will go will go what one thing you notice one thing you notice All the numbers that you have are all there Sen is divisible by 7 to something Sen Something here also, the numbers that are coming for all All will be divisible by sane so what x you can you focus this can you focus this You can see if you assume that you have replaced n 5 kept okay so 49 5 - 1 4 so friends this Your Ga 4 49 4 You're Done 196 49 4 49 36 16 17 16 wait a second did I do something wrong 49 * 4 4 9 36 No 169 196 That's what I think This is the basic map, isn't it, it is 196, now you Notice that these are some 50:50 gaps. There are things coming in which by consuming you It is going to be divisible, you are watching it 100% The numbers you are getting here are yours. If you are going to be divisible by seven, then brother You see that whatever is in x All the elements will be in y There will be only as many elements as there are in x All of them must be in your Y. You can try this Once you've raised 8 to the power 51 is 21, right? Okay, so what will you write later? since every element of Ekas Every element of ec is inva there four x is a subset of X is a subset Okay, let's see what you said next. Bhaiya, this is a set of divisors of 68. of B is a set of prime divisors of 68 Now look what is this brother, what is this brother The set is divisors of 68, meaning in this Your divisors of 68 will be written as B set What is your prime brother B set? divisors of 68 Prime divisors of 68 apply your mind Friends, here are all your numbers. Those who will come to Did 68 will come here only Those numbers will come which divide 68 But if they are prime numbers then All numbers that divide 68 are prime Think about the numbers that divide 68. Whatever number is here, will it be here Whatever number is there here which is 68 That father-in-law must be dividing prime numbers It will happen here also because here all Are the numbers prime numbers or composite numbers? Or your forest is fine here they all are Here are the numbers that divide 68 Pay only prime number state to divide If you do it, whatever the numbers here will be All of them will be present on this set too. All elements of b will be in the set a of b If all the elements are in the set a then b is a subset of a I understand for sure what you are saying Brother, what are you saying, brother, you are saying this Friends, it is easy, there is a set in which six are elements then power proper subsets of a How many proper subsets will there be of a mean Subtract this set into two proper subsets, brother. This set itself will be a subset of this first How many subsets will there be 1 2 3 4 5 6 to the power of 2 6 means 64 in that one minus 63 subset one Why minus it, you know that thing So let's answer many questions together. I am also putting it on, come on brother, now it's Wayne's turn Diagrams are very important. Interesting, you will enjoy it brother, okay one What is a diagram? Nothing but elements. We show this with the help of a circle and We can call the universal set using rectangles. Let me show you the Venn diagram What happens and why should you use it? I'll understand in a while, okay Guys, as if I have a universal set is from the forest Laker 1 2 3 4 dot dot dot 10 So far so good I have a set a which contains elements is 1 4 5 okay I have a b set or let's just take a set that's all right Now look at the universal set, you will see a rectangle. you show it from okay and the good brother a is A subset of the universal set is a context All sets are subsets of I told you about the universal set. And the universal set is the super set of all subsets of all those elements that contain does what all the other sets have, so this Rectangle denotes your universal set. and I will draw a circle inside it. The circle will denote your set A. From the circle we People denote small by the smaller set. Meaning those that are smaller than the universal set are okay. Now look, you are getting one F and five in this. Fur and F are coming, rest all 2 3 6 7 8 9 10 must be here somewhere Is this understood in the universal set? All your elements are in it You have 1 4 and 5 coming in the set 1 doti 4 5 6 7 8 9 10 These guys are your vein This is called a diagram. This is your forest diagram. It is said that if you believe in this, if you believe in this I'll give you the B set too. I gave you the B set. Setting the Focus 4 2 Now if I ask you to make a Venn diagram If I tell him how will it be done, he should pay attention to that only. What will you show with the cheese rectangle? What will you show Boss A from Rectangle Brother, what will you show with the rectangle, boss? Rectangle will show you the universal set Universal set okay now because a and b Now because oh well, I just said this I didn't explain it to you, let's talk about it later. I will come friends, I just told you I did not tell you about intersection etc., I will tell you about it later. I'll tell you after 10 minutes, okay, let's go. Let's move ahead, what are you saying brother? Now we have to understand friends, operations on Sets mean learning to play with sets Like in maths, we have plus minus etc. If you do, then friends, what is the meaning of union? It happens, just pay attention, it's okay, simple Union means and And intersection means and I will tell you how you can understand this. what does that mean okay as if my have a set say I have a set 1 2 3 okay and let's say I have a set b is 2 3 4 5 6 Well if I ask you what a uni b Union you and u sign to denote something If I ask you a uni b This means elements that are in a and b I am in a and b means I am in a also and means a and b means elements of type a and also of type b Elements finished, okay, now pay attention. So two elements are common in both. If I write it only once, I will write 1 2 3 Write down two 1 2 3 write down 4 5 6 this is your a This b is here now I'm going to learn to play with sets okay intersection means a and b should be common in both Common then an intersection also means union of Basically it's the opposite, okay, something like that made an upside down u a and b means a There should be 2 or 3 such elements in a and b. which is common to both a and b It's easy, I don't think it can be easier than this. If possible, you people understood the meaning of union. You guys understood the meaning of intersection, next The operation goes very easily brother. What does difference of sets mean? Okay, so let's say I took a set of 1 2 3 4 Suppose I took a set 4 5 6 Pay attention or else 4 5 let it be 6 Okay, if I ask you, what is the difference between a and b? I ask it means all those elements of a watch are not in be means be remove elements from a elements from b remove remove elements from a to b then all Write the definition of those elements at once. I give all that all those elements of a are not in b elements of a that are not in b which are not present in b ok boss ok So what are the elements of boss a like this The element which is not in b is of a such that element which is not in b simple gives you a I will also give you the formula, let me tell you about that. So what is the element in a that is not in b? There is a forest of a that is not in b So I'll take one here, two what is in B If not, take two, three, what is in B? If not, take three, I will take four. If it is in friends then b is removed from a, this b I have removed the part of b, brother I don't want b. Bhaiya, your a-b will come to 1 2 3, now if I Should I ask you b - a tell me boss then all those Elements of B which are not in a meaning B elements of that are not in a or Specify the elements of b and remove the ones from a Remove the ones from b to a from that, then b to b to four removed because four is part of your a So b - A friends your 5 6 will come clear Yes, I understood the matter brother, then you You have also understood the meaning of difference of sets. What have you done brother, I have understood, let's go So with that, friends, let's move on. What are you saying brother, cemetery difference Off sets now what is this operation simple See the meaning of symmetric difference. Triangle denotes it by triangle that a triangle is b doesn't it say something like that what does that mean to you okay like I took a set okay 1 2 3 okay I've taken a set of b, let's say 2 4. You understand what a - b is. a - b what will happen if you remove b from a then remove to Remove the two intersections and 1 3 gives 1 3 a elements not in b b - a Meaning if you remove a from b then b will be minus Your four will come a triangle b means a - b of a - b What did you understand with the union b - a Just make a union of these two, brother, this is one This is a set, what is the union of both? will be union will be 1 3 4 union meaning I understood all the elements 1 3 4, I understood. Boss, okay, so if I tell you a triangle If you remove b then a triangle b means a - b this b - a okay let's move on now Compliant means if I I bought sets 1 2 3 and a universal set. taken 1 2 3 4 dot dot dot dot as if up to 10 natural numbers okay if I say to you Compliant of a a compliant Basically, you can subtract a from the universal set. Two such elements of the universal set that If there is no part of a then it will come to you a Compliant means replacing a with b Compliant In case of What does disjoint sets mean? Yes brother, this is not an operation now. Learning what a disjoint set means So okay, what does disjoint set mean? Yes, just learn that, pay attention, this is okay There is no operation, I am telling the meaning of disjoint. hmm okay let's go disjointed means your a Intersection B F will come, meaning anything common If it doesn't happen then for example, suppose I have a I took a set 1 2 3 I took a set 4 5 If I ask you what a intersection b Friends, what is common between the two? If no element is common then this is your problem. This will come, if your fee comes then this is what we call it A&B R Dis Joints what does it mean that a and b are disjoint sets I understand disjoint sets, now they are joined Look at this, show it with a Venn diagram. You will enjoy it, okay, as if it were your universal set. Brother Universal Set Your One In This Case Universal set your Universal set your Tooth dot dot dot 10 okay pay attention focus focus okay it'll be fun okay So friends, I know I have two are sets A and B, then A is a sphere and B from a sphere now here's a thing Now pay attention to one thing here. pay attention to this Hey brother, pay attention that this is a set, this is B is a set and it is the universal set then a set I am your Natu and Th are coming B I am your Four and F are coming, rest 6 to 8 or 10 are yours. coming to the remaining space okay this is your I didn't draw a diagram of this, okay, but But but but right now it is disjointed so this means Not connected Not connected means if a and B have nothing in common, so they both The sphere will be formed separately but if it was common So their sphere becomes a connected joint like this A set is formed, for example, by a question Let's say I have a set of 1 2 3 Suppose I have a set B 2 4 Okay If I were to draw a Venn diagram of this, look. Universal set you denote by rectangle Two brothers, anything can happen, right? You will do this by adding both a and b. created okay this a set this b set so in a yours is 1 3 b in yours 4 and in both which It is common in both and will come in between 2 1 3 2 4 Do you understand what I am trying to say? I understand what you are trying to say Friends, I will show you all these things. Okay, so what are some basic questions first? The boss is saying that he has given you a universal set. is given set A is given set B C set is given to you, some things It has been asked that let's do one thing, in this everything Let's not do it then a Compliant a compliant I understand what the second one is saying. Boss B Compliant This is a very easy question for me, okay, the third one. Take a look at what you are saying Intersection of c Complaint is coming in four in both I am coming in both, three in both Write four 3 f in both, 4th is the same thing Now what did you say about intersection C? Compliant This means that by combining these two, even the forest Two will come, three will come, four will come I have taken two and four, please write 6s and 8, understand. Got it, now if a and b If you remove this from the complaint then 1 2 3 4 6 8 1 2 3 4 6 8 so 57 9 will be left so this is your 5 7 9 will be easy in my opinion, very easy fifth please do what are you saying Compliant Of Compliant So it's like I made a complaint Look your coming 5 6 7 8 9 5 6 7 8 9 come I was paying attention now If even this set of Compliant Of Compliant I will make a box here, answer it. I'm fine and make a box here, answers. I'm okay let's go to the sixth one. What are you saying, first remove the b-c So b - c means such elements of b which are in c If you remove c then 2 468 is common. Which is four common, six to 1 and 8 T and 8 will come, I understand brother, both have common What is common in both is fur and 6 so b Subtract 4 and 6 from the 2 and 8. what did you say b - ka compliant so 2 8 removing then two and 8 removing 1 3 4 5 6 7 9 1 3 4 5 6 7 9 2 3 4 5 6 7 8 9 3 4 Pa ​​6 Yes, that's right, I just cross-check it sometimes. There should be no room for error Got it easy I hope you operations Clear the basic questions on the on-sets Now that we have done this, let's do another question based on this. Let's do something interesting, what are you saying? You've been given a set roster of something like this. Write it in the form brother, enjoy the set builder If I don't know, what a set has been given, x is true, that If x is your natural number then brother x is your Natural number is how far the infighting will go is it true that x is your 2n and n is your natural number so x what is your n equals 2n If you put one in place of n as your natural number Two If you put two in place of n, you will get four instead of n. If we put th in place of n then 6 will come. If we put 8 in place of n then t will come. So you understood the logic, basically like this Friends that even number 2n your always even The number denotes and this also continued Why will it go to infinities because Bhaiya ji Because Babua ji, what is happening, brother? What is happening brother, did you understand, it's okay? C okay 2n one is your 2n - 1 guys This is your even number minus one from the even number. If you do this, your number will always be odd, this is basically It is a set of odd numbers, if you don't understand n is your natural number, replace n with one, then Put two, then three, then four If you extract the values, then keeping the first one gives one. It will come if you keep it, it will come, okay keep three But your F will come, on keeping F your S will be like this It will keep going, it will keep going, this is yours. It will be set and you will also be given a D set. Hey D Set, what did you say brother, it's true that x Your prime natural number is a prime number is also a natural number and is also a prime number It is also a natural number and it is also simple friends If it is there then it is yours 2 3 5 7 11 Basically prime natural numbers 13 17 19 okay 19 will become 23 keep going It will go well, okay, very good, so you have used logic. I have written it, now what are I saying to you? Intersection B Tell friends A Intersection B means common in both so in these two Think and tell me what the common elements will be. Look, it has all the natural numbers. Even natural numbers in it It contains all the natural numbers and it is even. If there are ner l numbers then I can say that this This will be a subset of this, meaning here whatever All the elements will be present here There will be as many elements as there are here All of them will be present here. If all are present here then both are common What will be your values ​​common to both? If you look at what is common in both of them common to both Four will be common in both 8 10 12 again common to both Four will come common in both, six will come common in both I will have common eight, 10, 12, basically all of it. Elements I understood brother, think for yourself and see everything here. Natural numbers are all natural numbers here But one natural number is common in both. What will come out of these natural numbers friends? Your answer will come, you understood the intersection. C so what is common in these two, all the odds are numbers all natural numbers so all these The elements must be present here. So the common thing between these two will be friends. I will go, use your brain, use your brain, set it right. is an intersection then an intersection d a Intersection D friends here as many All the elements are present If so, this intersection will be yours. I will come, I understand, okay boss, look here, okay let's go. So it's over, this is your next thing. No, this is done, come on now friend, let's answer this. tell me what are you saying focus focus Okay, just pay attention to what I taught you. b is a subset of a b is a subset then both Intersection b is coming, do you understand this? What happens friends, you just have to understand that If a is a subset of b then a is the intersection of b Brother, if a is a subset of b, it means all the subsets of a All the elements of a are present in b If elements are present in b then or friends What are the common elements in both? If you understand all the a ones then it is a intersection b friends your a will come, understood friends if a is a subset b means all the elements of a If all the elements of a are in b then a or b will be your b, are you able to understand this? If all the elements of a are in b then If you want to take elements of both, then a this b b will come, look here all of a Note that elements b contain all elements of a. elements B contains all the elements of A I think of you as if A is your two. B your t is 3 so all the elements of is in B means A is a subset of B. of B all elements of A in B all elements in b then a is a subset of b Okay, so tell me how much will A minus B cost? a - b then remove elements from a to b What is common between the two? Remove 1 and 2 from here. So only f will remain so remember if a is a subset of b If all the elements of a are present in b then All elements of a will disappear. Friends, this will become your logic a-b. I understand, okay, let's move on. Let's go, what are you saying, it's very easy, look. Answer: An intersection of a set is Intersecting it with the Fa set Friends, your F-Setti will always come F-Setti It will come, there is nothing common between the two, friend. The union of A with F means a set And there is your Fa set, in it any If there is no element then brother all the elements If you want to take it then only your A will come, okay A's Intersection of A with the universal set Intersection with the universal set is always a Remember that A is always a subset of the universal set of all elements The essence of the universal set In the universal set, what is common between the two? There will be something common between both of you friends. Uni A Uni Universal will come from Universal Understand Come on, what are you saying, it's already ours. Let's give it a go now now now now I don't want to remove it now, my van I want to explain to you how to make a diagram. on the diagram at at at before your Let's take this question, a uni a Compliant There is a set with no understanding always Take an example, there is a set 1 2, suppose The universal set is 1 2 3 4, say It is a universal set, okay, easy, so look at it. and a compliant Now if I tell you a union of sets do a The complainant was neither a union nor a a compact universal set is Now look, the compliant thing of F is F. Compliant I only know what this thing is This thing is complimentary to Pi. Note Do it, it is a very important thing, okay? Except removing the F, then just F from the universal set If you remove it, then the entire universal set is It will come, okay, what are you saying now? Now what are you saying, just look at what it means Universal set of universal sets Intersecting with a universal with a doing the intersection of the set Friends, that will be your a only, okay a ka Intersecting a with a compact If you don't understand then A of A Complainant's Complainant Compliant and universal set of Karna F Compliant of If nothing is left after removing it then this is your problem. Would Okay, so basically what does that mean? Universal Set Compliant here Doing section with a so fa's Intersection of f with intersection a Friends, this will be your F, understood it? Your result will be common in both, okay something galti to nahi kari a unin a Compleños is it okay to do what are you saying question I Dr Appropriateness read what are you saying a This Bee Ka Compliant Make the universal set into two sets If it is being done then make it a and assume that Let's assume you have joint sets, okay? This is your universal set, this is your a It's done, it's your turn, now what do you say? are friends a union b a union b union b would mean a k all and b k b understood a unin b all Let's take some of the a union b and you take everything Now you include it, but what did you say to us? a y b excluding What will be left after leaving a and b? If I leave this part out, the rest is If you understand that a part will remain, then how do you shed it? I will show you what you do, the rest is left. Don't forget to share this part friends, this part is over. This is your A or B ka complinos Look carefully, this is also one of your formulas. It is possible that a law of yours should also be made now. You will understand, okay, you have to focus. okay take it easy, it's absolutely fine so I Let me make it different here, now let me have one Compliant A set and this is your B set, focus on this Your A set is your B set. A compliant. here neither Compliant What will happen friends, please And he understood that he left B and left Diya, what are you saying now, what are you saying now Friends, understand that both of them are brothers. Compleños What is the common part in both of these? What is common in both? Is this one common? Is the orange part common? The part is not coming here, so this orange part Isn't it common? This is orange. This is orange. It's not coming here, but if you look outside, it The part which is outside the sphere It is shaded in this as well as in this If you understand that it is shaded then you understand the common part. What will come, will you have a common part in this? I make it separately, I make it above these The common part of both will be your focus I have to focus, I have made a circle The sphere made will be your common part in both of these You will understand that this is common in both of them. You will understand this common part, now notice one thing Now notice one thing, this is also the proof. De Morgan's Law is that De Morgan's Law Friends, the diagram here is the same The diagram is here The diagram is here the same diagram is here so can I It can be said that A is the union of B Compliant B's The diagram of the complaint being made A Compliant So different Separate complaint section Now change it here, take a look at it. Let's make a diagram, friends. So a How does intersection b become intersection a? take a look so this is what I made this I b made okay focus focus focus So let's do a intersect b. Except a intersection b this will be brother both This will be the intersection of this excluding this leaving aside Compliant I skipped section B, I got it, now look here. a compliant Pre-built b compliant Focus carefully, okay, focus completely. The focus is fine, look here, it's fine, the color is good brother Come on, I want this too, I want this too brother What is this here, so shade it. what's here so shade that and The outer one is also shaded, so such a diagram It will come, okay, the diagram is coming here. The same diagram is here, so can I can I say that can I say that What is the intersection of the two holes? Complain, friends, these are your two Ds. Morgan's laws are what I'm talking about now. I will use it in questions so that you understand. If you have better understanding then just remember How to keep it friends, this is your D Morgan what is this law this is your de morgan law I will tell you in a while, but leave from here. I was teaching you how to draw a forest diagram. These are your De Morgan's laws, okay? How will you remember at Union Intersection? Changes and intersection unions Changes take place and Compliant Compliant Compliant Formulas are based on this formula Very good questions you should ask from this chapter. Please pay attention to what is formless Is Boss formless? Is Boss paying attention? Okay, here are your cardinal number formulas. What is the number of elements in a or b equals the number of elements in a plus number of elements in b minus number of elements in a intersection b good one Let's do the work first so I replace the formula Let me make some more forest diagrams so that Let me understand you better Make it, show me, make it, everyone a - How to make the th diagram of b You have taken universal care. give you took this you took this this is your a This is your B to a my B what does it mean The elements of A that are not present in B So we're talking about the elements of A, which which is not present in B and is present in B There is no diagram, come brother, yes it's okay. Friends, basically if we say this, it means both of them. O brother, if you had said this here, you would have said only this. So what did he say about the shade A part? Remove B from A. Remove B from A and you will understand. You are saying that I have removed the B, now I understand. What happened, just saying a while shedding It shades the entire A circle but If B is to be removed then whatever amount of B is coming in A As much as it is coming, I have removed it, this is yours Friends, a my b is done, from here you You got a great thing, my friends. My B happens okay let's tell the next B My what will be very easy be mine what It will be very easy, very easy, very easy, just like that Friends, something will be made, just look at it, same to same. Pay attention to what will happen with B minus pay attention pay attention pay attention okay So then so y your A set y your B If the set is okay then B would have said it and he would have done both. But if A is to be removed from B then the amount of A It is coming in part B, remove it, it is removed. So this is your b-a, this much part of yours b - a and friends what do you call this Listening a - b is also called only a and b - a will also be called only b, only b I am talking only about B, understand It's clear boss, let's try one more. Show me brother, as if I said a intersection b So this is very easy to make a intersection b What does a mean intersection b mean What is the common part of a and b? Boss, what will become the common part? The boss who is in A is also in B who is in A It is also there in B, this part is fine a yian b what will happen boss a y b a and b all the elements of a and all the elements of b elements pay attention pay attention bus bus bus This is the last one, okay, I mean, of this part. This is the last chapter, let it end a little. I will go, okay, I understood, now pay attention. Now derive your formulas from here too If I ask you If I ask you May I ask if you are paying attention here? What is this brother, please erase it. Why should you be unnecessarily confused? You should remove it. Don't get confused with The Faulty OK with this and here you can delete it. Please delete this here, confused It's not going to happen at all, what are you saying? are the number of elements in a formula What will be the number of elements in this case? in a uni b then number of elements in a plus number of elements in b minus number of elements in a intersection b in understanding Think for yourself where did this formula come from? Look, if I ask you what a uni b How many elements will be there in then the number of elements in a plus number of elements in b but when you did the number of elements in a When you calculate the number of elements in a This part had already come in it, this one Part had come Number of elements in b If it is done then this part will come again in it. If this part comes back in it then That's why it's important to do this minus once. Intersection, so what is your formula? Given that the number of elements in a unit b is will be the number of elements in a plus number of elements in b minus number of Elements in a have common b mean intersection b Okay, now look here, if the number of elements in a uni b number of elements in a plus The number of elements in b is equal to its I mean, obviously, this is your zero and Number of elements in a intersection b means a single element in intersection b No means there is nothing common between a and b means a and b are your disjoint sets So the same thing is written here, okay? Let's look at the number of elements a - b. How will this come out very easily in a-b How many elements will be there in a elements is the number of elements in a What to remove from that, two intersection people. Remove the elements brother, that's what we do when When you do a - b then a You look at the elements and from that you get B. Do you remove elements or should I say a From the element you have the intersection of both If you remove the elements, the same thing is written So what is written there, boss's number? of elements in a - b will be the number of intersection of both elements in a my How many elements are there in and the same simil What will be the number of elements in b - a number of elements in b minus number of Elements in a intersection b is clear now How do questions based on this come? First, let's consider what he is saying. very easy if a and b are two sets true that number of elements in a 17 is the number of Elements in 23 is the number of elements in a This is B 38 What did you ask yourself a How many elements will be in intersection B? Do you understand the formula? The number of elements in a union b is is the number of elements in a plus the number of elements in b minus number of elements in a intersection b then you get the number of Elements in a and b are known to be 38 in number. of elements in a you know 17 is the number of elements in b you know is 23 How much common do you have to find out between the two, brother? If you want to withdraw then it is very easy 17 + 23 40 So this is your arrival 38 This is your arrival 40 This is the number of elements in a Intersection b take this thing here so plus If it becomes then the number of elements in a Intersection b is 40 - 38 2 so both How many elements are common in only and Only two elements are common right now What did you say about the number of elements in a - b? Friends, how about the second one? will give the number of elements in a - b of this Meaning basically it is only one thing You are doing it, you mean just do one thing only a's only a's elements tell which is unique for a which is unique for a be faithful okay so number of elements what will happen to these a - b boss number of number of elements in a minus number of elements in the intersection of those two so The number of elements is 17 in a and both There are two in the intersection of and only How many will be there in just a only a 15 Understood the elements, these are 15 such elements which is not present in B. What did the third say? Third told you the number of elements in b - a then number of elements in b to number of elements in b intersection a minus do it So say b intersection a or a intersection b If you say the same thing, then the number of elements In B yours is 23 this is your two common so 21 elements came only in b Meaning these 21 elements which are present in a No, it is present only in B, what did you say? Number of elements in exactly one of a and b number of elements to be extracted e in Exactly either in a or in b means it Basically, this is what fourth means, basically. that you get the number of elements in a triangle tell B is okay number of elements in a triangle b tell me what it means is a triangle b what was boss number of elements in a - b plus number of elements in b - a okay means number of elements in exactly one of a and b means the number of elements that are in A only be in A plus the number of elements that just be in B okay so just in A there's 15 You have 21 in just B so 21 = 15 Friends, this is your 36 36 aa Gone okay 36 such elements only one one is a part of the same set or let A or B Let's do the next thing, what did you say, now this is very This is an interesting question, well before that this Let's do what you are saying in the question if A and T are two sets such that a h 21 elements t has 32 elements a Near intersection 11 This is very easy Friend, do it in your homework or check the comment box I will definitely tell you the answer, it is very easy. Given intersection t has 32 and s has 21 It couldn't be easier to remove this You can do this and show me what you are saying. In the question, let A and B be two sets a has 35, a good number of elements in a written 35 means 35 elements in your a It is part of the set but that doesn't mean it That this is just one part, do you understand? What is happening, am I understanding what I am saying? I am telling you brother, if I tell you that You study with me, that means It would have been a bit like you would have studied only with me. Think about it, maybe you're someone outside I have been studying since then, you understand me what am I saying okay so if 35 The elements belong to a set so I simply did this You are told that a set has 35 elements. from here don't think that 35 elements Only A set may be among these 35 Some of you are double faced brother, some from different sets There may be a part, maybe three or four out of 35 Element b may be part of the set a Out of 35 elements of the set, 10 elements are I understand that I am part of the set. What I am saying means only this It just means that it is clear that a Both sets have 35 elements. There is 11 in the intersection, well what did you give? is a yin of bi Compliant After removing that, it will be 17 whenever I see you now. Whenever you are given this thing, understand what I say. Whenever you are given this thing, you can do it from here. Always keep one thing in mind, what is a or b Compliant Friends, I told you the formula of a and b. How do you get a complaint Universal set minus that set if you get a Compliant in a Compliant Minus number of elements in a simple as If you say a number of complements, just tell him Minus the universal set and it's over okay so basically the number of elements in a Union B's com 17 diya hua hai number of Elements in the union universal set is 57 What did you get out of this? will give the number of elements in a or b Okay, so if 57 comes then number off. Elements in a union b your aa understand What did he say, take out A B and then A formula We know that A equals B. a p a b ps a sorry mine A is the intersection of B so A and B are 40 You have 35 n b you have to remove you At the intersection of the two you have 11 elements is Okay, so 35 minus 11 35 minus 25 24 6 will come friends no 14 come friends Your Number of Elements in Your 14 How 35 my 114 24 went here 44 What are you doing in mathematics? 35 24 4 okay so number of elements What will be the simple number of these a - b Extracting Elements in Difference of Sets then the number of elements in a minus number of elements common in both of them then number of elements in a you are given 35 at the intersection of the two 11 okay so this Ra 24 so number off Elements in a - b 24 means now you understand that a set has 35 elements but may These elements are duplicates from another set There are 11 elements that are also part of the B set. There is also a part of A, if you understand then just A Who will be the part of only A? Who will be part of A only 24 people 24 I understand the elements, I can do it I think you should do this as homework. It is very easy to take it I am giving all the questions that I have to answer It's okay to do it, I hope you guys enjoy it. He must be coming now, let's move ahead boss. Next question is something like this one. Now look at what he said in the question. Where do you apply for this application? Is in a group of 400 people 250 can speak Hindi 200 Can Speak English How Many Can Speak both Hindi and English now attention What did Dena tell us, there are 400 people, this means What are you basically being told? A universal set is being given, you understand. Yes, you have a total of 400 people, which means this is your Universal Set Your 400 Across the Universe People are saying something like this in context There are 400 people in me, out of those 400, 250 speak Hindi. They say this does not mean that 250 is just They speak Hindi, maybe among these 250 You speak some English as well brother, apart from Hindi. Some people also speak English. 250 If you speak Hindi, it means You should not think that 250 is only for Hindi. They say no no no no I understood 200 people speak English, this means Not that 200 people only speak English 200 people speak English, meaning maybe Does anyone else among them speak Hindi or something? And you say okay how many can speak How many people know both languages? Can you tell me how they will extract both the words? can mean intersection common you like this Imagine the number of people speaking in Hindi. 250 are the number of people speaking in English Friends, there are 200 people and because we are here But if such a thing is not given then we will accept it and proceed accordingly. Is it that all the people there are something or the other? We are speaking Hindi and English as long as we This should not be asked in the question that brother Yes, it is like that brother, look this is your number off Elements in universal set hota per Because because in this case our This was not given to anyone, not mentioned in the question I noticed that everyone was saying something or the other. You should assume that everyone is something or the other. I am speaking Hindi and English, which means there is one such thing. I am not a human being who knows neither Hindi nor English. If he is saying okay then it means friends This will be your h y e everyone something or the other You are speaking Hindi and English, yours will be 400 Now what did you ask such people who say both If you are there then what is the formula from us Asked people who are also speaking Hindi Both of them are speaking English as well. I have asked about intersection, you have understood it now. You can do it with the formula, Wayne. Try it with a diagram. Try it with a Venn diagram. Look, the answer comes very quickly, so Wayne Diagrams are also taught in competitive exams. Lots of questions based on Venn diagrams You get asked a lot of questions, okay? So how do you remove it? You know, this is a union. B happens to be A intersection B happens to be what happens is it's only a and it Only B happens now I will tell you everything How to draw out okay focus a little fun Will come friends Hindi speaking person is 250, AB na bole ke This is English Hindi Hindi English okay So Hindi means here you have 250 here But you have 250 people, now you understand this, right? And English, these are your 200 people. Tell me how long ago the common Good to remove this common thing friends You have to find out what you want to remove. How many are you saying common, there are 400 in the union Now attention Union means you have 400 in this whole You have 400 in total, okay, now what should I do? I will draw a Venn diagram Before I explain it to you, first take it out of the formula. So what are you getting from the formula? The formula is very easy brother that n h union will be equal to n Hindi plus n English mine h Hindi Intersection English to n Hindi your 200 not people 200 50 people or not your 400 These are your 200 people. You have 400 people in the union and these You have to remove the intersection and focus. Okay, so 250 I 450 400 there 200 50 There will be people who know both Hindi and English There are 50 such people talking, I understood. Gone now listen now listen okay so here Those 50 people who talk to both of you come. Went 50 of your people who speak both languages You have come, now understand how many Hindi speakers there are. 250 Out of these 250, there are 50 people who Speaking English too Yes, I will say it again, out of these 250, these this here here here this out of 250 this out of 250 50 people who also speak English So if you subtract 50 from 250, that You are speaking English, meaning with H, if you If you remove the intersection e, you get such people. Those who speak only Hindi will go Those who speak only Hindi, talk about this one. I am a Hindi speaking person, how many of you are? There will be 200 people minus 50 from 250. Diya English speaking people speak English In which some people might also be speaking Hindi. There are 200 people, out of these 200 people, if you Subtract 50 from those who also speak Hindi. So only 10 people who speak English come I understood what you will go and now you will see. Inter Union Kya Aayega 200 Plus 50 250 PS 150 400 Okay guys, so here's a little diagram for you. It should be understood from this as well, neither from the diagram nor from Diagram from the majority of the question we people Let's do this question first. Then we will go to some lodge and Then I will continue with the question, okay? What are you saying friends if A&B R Two sets u is the universal set y in the set There are 700 people A has 200 A B has 300 A intersection B has 100 to remove you How many will come in this, how will we do it Bab, I don't understand it whenever something like this happens You should remember the compliment given by me What was it, D'Magan, what did I teach you? Look at the intersection, you can see this How to break a hole complement taught you I was as if n Compliant Union the section and the hole Compliant Did I teach you or yours from Saab? Friends, De Morgan's Law, now this is your two minutes. I'm about to come back again, just a little bit. Keep this in mind for now, will you? Friends, if there are different complaint sections Different complaints have been received Do and Compliant Did it happen, does anyone know the formula for it? of any thing minus that set from the compliant set You give me a compliant set, I know it. There are 700 people, take out a or b, now this is for you. If it comes then how will we find out n or b A y B means a ps a b minus a intersection b then a Union B yours has come a meaning 200 A B mean 300 A intersection B mean 100 then 500 400 has come friends A Union B Your 400 rupees It's okay, just take it out here now. What can you take out here, it is a universal set There are 700 people in Union A and 400 people in Union B. If yes then the answer has come, what are 300 people? Compliant Easy Boss Easy, I think let's go with this one. I will ask the questions a little later. Some people think that this is a very easy law. What would a or a a be its own ideal potential Los speak very easy a intersection a too a means union of two same sets The same set will be the intersection of two same sets Do the same set and lose your potential. What does Identity Law mean that you are taking Whatever is there should come, whatever you are taking should come. If a set is taken as its union with f So only a will come, it is a simple thing, try it. intersection of a universal set then a If it comes then what does identity mean a taking a will come a taking a come will go then a The intersection of a universal set with because you know a is a subset of your is the universal set of all elements of a are present in the universal, then both In common a computer law is going to come Did you read in childhood that do a y b or b uni a do the same thing a Intersection b Do b Intersection a Do a That's it, okay, so this is your idea. Important Identity and Cumulative Log What was the meaning of associative, this was also childhood What have I done, pay attention to it It will be important, I will tell you here. Okay, the next two are important: do a and b. and then union it with c or First do b or c and then their union a Same thing with intersections too Same thing union and intersection Same thing is going on in Associative now If the distributor is important Remember in the distributor if I wrote was a * b + c what does it mean a * b + c now this is very important which It is important, I am telling you this. Your importance is very high. And this is very important for you. It's more okay to focus a little bit if I write a in b p, people know a in B will be Ps A in C will be this It used to be childhood Your distribution continues as usual what are you doing here a y b intersection C so simple A yi B with even I understood it with A Y C too, I understood it brother. Got it, got it, from a to b to c then from a to b with a y c with a y b with a y c with a y b with a y c and in between I have placed an intersection, this is yours Check out the distributor law here. If the intersection is outside a then the intersection of b Look at the same thing with a intersection c So a * b a * c a * b a * c a * b a * c in the middle plus so a intersection b a Intersection c between union understood easy And I just told you about De Morgan's Law. Hole of Union Compliant section hole Put a complaint in it. De Morgan's laws are correct it's ok Boss, okay, boss, I think it's okay. So, these were some basic losses of both of them. You will be asked a number of questions based on I will get you all done today There is no need to take load and tension, boss. Let's ask this one, a very good question. This is a very good question for you in school exams. big enough to be asked in There is a possibility, so what are you saying? What are the sets saying in the question a and b have three and six elements Respectively the cardinal number of the set a That means how many elements are there in it, it is three. How many elements are the cardinal of the set b? Bhaiya there are six elements what can be the Minimum and maximum number of elements in least and most least and Maximum means minimum and maximum The value asked is a intersection b of attention I will give you the correct example, you can do it also. But you don't have to do it by example, you just have to use your mind. Put the first one, okay friends. Intersection B has the first wa asked what asked us two things Maximum Maximum A Intersection B How many elements will be the maximum number of Elements in a intersection b and and and Minimum number of elements in an intersection B Okay friends, talk about the minimum first. If we take it then at least how many elements means less What value can be less than a Intersection B has three elements in it It has six elements, it has three elements It has an element called intersection meaning common. Put at least some value in both. How common can it be? one element two elements three elements array It is also possible that even one element is common It may not be possible that A is any set B is any If both are set and there is nothing common then Minimum Zero if there is nothing common between the two The smallest value is the smallest value Intersection B will have a maximum of zero. What What will be the maximum common value? It can happen if it has three elements. It has six elements These three elements are here too, father-in-law. What did I say, these are three elements. If the father-in-law is here too, then how many are common? elements will be three elements from this There can't be much in common, why do these two I have a big number six, don't even look at it. If the younger one is Three, then he could be Three's brother. There must be one element in three that is here But if it is, then one element may have become common. There should be two elements among these three which are either Two elements may have become common; all three may have become common. If it is on Y then all three are in both Elements have become common, now there are four If the element is not there then maximum four Elements cannot come in common, maximum You can have three common elements, understood? Okay, now look at this, minimum Value is at least the value of A union B What will be the maximum What will be the value of A union B? You can think in two ways or just one. think in a way, it's a simple thing, okay Friends, a y, well n is not written at all, a y b a y b ok It has three elements, it has six elements at most a unin b Meaning both elements What is the maximum value to take? What could it be that it also has six elements? Let me write it and write three more of this What's more, should I write six of this too? I will write three more of this separately. What will happen is that the total maximum will be yours. elements may be in it okay you You can also think that when these two Nothing in common then a union b maximum I got it, I got it, okay, look here. What can be the minimum value? What is the minimum value that can be When these three elements are coming here also So three elements are common, so three Elements are common Three elements are common So you will write three of this and three of this back. will you write it down I will say it again if if if this All three elements are present here. If present on A or B, then the element is You must have understood what I am saying, did you understand? You can understand what I am saying Bhaiya, this minimum will come then, this minimum will come then When A intersects B, your maximum I understand that it will come and when will this maximum come when Your A Intersection B Minimum Can you think of anything to say? I wish I could put my mind to you again I'll tell you once 2. Assume A told you T 3. Assume B told you said T 3 4 5 6 ok pay attention B K Let's take two cases and B tells you B tells you said 4 5 6 7 8 don't pay attention pay attention If you don't give it then first assume you have taken both of them now. In both of these, all three elements of A are here If the union B exists then what will happen when it is All three elements y are present on A union B Yours will come Tooth 4 F 6 see it is coming equal to B These elements are coming in the next three of them. If element is at y then six elements will come at y If you understand then this is what can happen minimum minimum A Union B Minimum A Union also friends ch Elements of Maya Understood When you have your maximum and when both have common There is nothing when both have something in common If not then A Union B The 4 5 69 Three of the elements will be made, not six of it. I was able to understand the logic, I was able to understand the logic, very good It was a very good question Okay boss, let's move on. Now friends, let's move ahead, actually I, you guys I will tell you one thing, I am very hurt It's done, friends, I didn't The entire video was recorded, meaning If there is another one and a half hour class left then that I had recorded it but I missed the end moment I saw that the mic was dead, so now I I have to record it again First of all, charge the mic for one hour at night. It's 5:30 in the morning, so but Anyway, I had to go to this lecture today so I thought Friend, let's complete this anyway. Friend, I will have to bring enthusiasm, I mean like this The enthusiasm ends completely but it doesn't matter. No, it means work is work, let's finish it. let's do it then move on okay let's go Anyway, friend, now we are very interesting. I am going to the party, I have read this. I have repeated the same thing, okay, let's go. Dude what is this now okay a intersection b Compt has told you guys, so how? Take out a Venn diagram, what should I make brother? Make a Venn diagram. Okay, so first of all. Brother, I made a Venn diagram, please pay attention. It's okay to give, I made him boss Wayne The diagram is fine, don't copy it. If you can, let's do one thing, right? You probably won't be able to copy it, right? Anyway, let's make one here again. And okay, why am I making two now? You will understand, okay, again the same thing. This is the concept of a and b, pay attention to it. Quickly Quickly Quickly Focus Three Why I am making it, you will understand where the tension is. Are you taking it brother, don't worry at all Take it, okay, okay, let's go, this is yours, this is your b this your a this your b this your a this your b now pay attention okay so these people What are these people saying, Banta? These people are saying that brother a a means this a means this b Compliant The thing is B except sphere B except sphere B Leaving the ball, okay, what did you say now? Intersection means common to both of them The region is the common region of both of them. Which region is shaded, can you see? He must be giving it here, it is completely shaded here. Pe A is completely shaded, here some of Pe A Part shaded so this one of the common region a The part has arrived, now what do I call it? I call him boss, I call him Should I say a-b or only a I say only A, I say, did you understand? If it is a - b or only a then your answer is done. a- B. Okay, now why is this important? Pay attention to that, I am looking at him again and again so that the mic doesn't go off again okay Anyway, let's see what's important here. Listen to me very carefully on this one thing. than this is equal to this this is equal to this This is equal to this This is equal to this This is equivalent to this one thing, you can do a lot All the proven questions have been answered, okay? So now we move on to proofing questions. We will do it, but before that note down a few things. Look, you understand that a - b means only a What does it mean to be a intersection b compliant? Can you see if a - b means an intersection? B Compliant Done and instead of minus there is intersection I'll say it again after the minus whatever It is written that whatever is written after the minus Compleños of place c Compliant Take section c. Let a - a be the intersection c now. Here also whatever is added after the minus Whatever is added after the minus What did you do with whatever happened afterward? Intersection instead of minus and a intersection of c Compliant Intersection instead of minus and a like Well, this logic is very clear to you. It is a very very very important thing There's something very important right here. Compleños First of all, you should work on this thing in the question It is coming, I understand, it is very important Does whatever is written after the minus signify Compleños I told you one thing to do. Two more things you need to remember What was the distributor property? Distributor Distribute Property What Thi distributor property what thi do You guys remember, just look, brother. Intersection B Union C If Written So what will become of intersection union? This thing that is placed outside will become B of B. Meaning a intersection b and this one that appeared outside This means intersection of S and B. I put a union in, did you understand this? Simple, you should know, don't you believe it? If a is the union of b and b is the intersection of What is the simple thing with c that is attached outside a union these b's also so a y b which felt outside a union these c of b then a y c and between You have put an intersection, oh brother, this is the same There is something even more important in multiplication, friend. It will happen through this too, I understand it very well. Well, this is your distributor. You should absolutely remember this property. It will also be useful to you, okay, secondly your D Morgan Law second your what boss second your Brother, what does De Morgan's law say? Pay attention to whether a or b is a hole Compliant So what will become of a compliment? What about intersection instead of separate and union? I understood it Guruji, it is very good, believe it if a Hole Compliant of Intersection b B's Compliant The questions seem very very easy those I understand, okay, let's do it now. I will show you, I will do three or four automatically. You can do all of this, okay, now just pay attention. It's okay to give in an easier way, friends. No one will tell me no one will ever tell me ever ever okay let's pay attention So look at the minus, whatever is there after the minus Whatever intersection appears later in place of Compliant Section applied after minus whatever it is I complained And this is your b compliant Section: Are you able to understand this? Guruji, keep solving a and b. This b is written as intersection. Now look at b. Compliant Ka Union with B Friends this is your Universal set is simple thing now here But let me teach you something important. Okay, it's a very important matter, okay. One more very very important thing to you It is important to learn it in the question of Pru. No, it will be applied in every question, okay, suppose if A if Hey, how should I tell you guys, okay, if assume that B is a subset of A if then A union B of B intersection or else this is our yes let's go okay A uni B what will come A intersection B what will come and mine be a little careful Look, okay, so if A is a subset of B. Meaning one set is a subset of another set The second subset means all the elements of A and B. All the elements of A coming into B so a yi b friends b will be okay my Listening A Intersection B Guys A will be okay and A mine B Friends, your F will be done, there is no such thing in A element not coming in b okay But this is of no use to me, now listen to me What happens if one set is a subset of another If one set is a subset of the other then You understand this little set. And this will be a big set, do you understand? Isn't it a small set, this is a big set? You can imagine it will be like this, this is the whole thing. If it is a part then it will be big, this is its entire If it is a part then it will be big, now listen to it, it will be small Union big always big comes small The intersection is always large but small. For that, one must be a subset of the other. I will give you an example now and you will understand it better. You just remember that if a small subset is the union of a larger set then a smaller set Always a large set A small set will come Intersection of larger set will always contain smaller set Okay, just remember to tell you this. I wanted to talk about something very important, okay? Now how will it be used brother, it should be used like this Please pay attention, please pay attention friends this and this okay this and this Universal set and this any set universal is a subset of a set, then you understand Which of the two is bigger, friends? your small set and of course your The larger set is exactly the intersection of the smaller set. Intersection of a smaller set with a larger set With the big set will always come a smaller set Look friends, your answer is a union b. a and b look at what your RHS is given by which is given by your RHS, understand Guruji, I am not able to understand much. It seems difficult, don't worry, I am here I won't tell you everything, you just keep watching and see what happens I replaced minus with intersection b of place b Now pay attention to the complaint section b Okay guys, this is intersection b. so a intersection b intersection of a so Don't apply it like that or else you are getting confused So this b Compliant Now look at section a intersection b like that Ka Vaisa Be Compliant What will be common, nothing will happen brother So this is your F, F is a subset of every set It means as if this would be some set of his There will be a subset, I mean, roughly speaking. The same thing that this is your friends small set or Your friends Big Set Small Intersection Big always small look F has come RHS I understood it well, boss, it's clear. Just look here, see what I said. minus remove intersection and whatever minus whatever is written after minus what did I do to him what did I do to him Made a complaint I did section B. Compliant If so, this a will not be able to go inside right now. I know what I've done, De Morgan. This is from the law Also of complement b and the place of intersection Union as I mentioned Marg Law also Now what to do is an intersection. will go in then an intersection a Compliant Section A Compliant Section B Compleños And this is your larger set minus the union of the smaller set With the big set, always the big set, so this Your a intersection b Compliant Minus instead of section Compliant We have to give its answer in the box as homework. I want to tell you what the minus is saying brother Intersection instead of minus and whatever wrote it after Compliant Friends, so an intersection be compliant. It's very easy, now look at it and solve it, tell me. intersection of ata to the minus b Compliant Minus section compliant Remove the minus and replace the intersection with B. Compliant Union B and your intersection inside so this Your brother a yi b intersection friends b Compliant of The intersection of the larger set and the smaller set is always small set a yi b is here okay do it You can do it like this brother, by removing the minus Complement of b instead of intersection b section b pay attention so intersection b inside went to a intersection b intersection b inside Then the intersection of b and b is such that It will go and just look at the intersection here. a Intersection b You know both of these Compliant If you do this, your homework will be very easy. If the question is then look at the same thing, union of a Kara is b minus so what is b minus one place I'll do the intersection here instead of minus b Pay your a Compliant Of Everything is fine and the intersection remains the same. So here you go, look at this intersection. Friends, the union of a set is a complement. Section always small set this had happened Come on, you guys understand what to do. Okay, so these proofing people are from you. Now we will go to four more questions based on this. If you do it in a slightly different way, it is fine. Just focus, pay attention, isn't it relaxing? From Okay, now let's see what you're told. If you were asked to prove it to me, brother He said, prove it, prove a = b means If you want to equalize two sets, how do you do it? I am telling you how to do it, what should you do? You can prove that A is a subset of B. And B is a subset of your A if you give this proof you declare that A is a subset of B and B is a subset of your A means A is equal to B If you understand this then this is the proof for you. What proof will you have to do? I have to prove this, I understand now. How to prove that A is a subset of B and B is a subset of A, I'll tell you, okay. Pay attention to what you need to do if you To prove that A is a subset of B, you What to do: Take an element that matches your A. Will anyone belong, I will do it one by one element lo ap acas jo apke a ko belong I understand, he will do it and give it something. something something something something according to the question Keep doing it, you will get that element in the end. It belongs to your B too, now you think Let's see if any element belongs to A. He is also belonging to B means a is a subset of b means all of a element brother if x then I random someone I'm taking the element and think about it and see if a All elements are in b if all elements in a element b is in a means subset of b is a is a subset of your b then I assumed that x is in your a if x is in your a x By solving yours, I also came to b, meaning a Your subset of b is every element of a Yours must be in B, if you understand If you just prove it then from here You will prove that a is a subset of b. I understand what you mean, but right now B is a subset. If b is a subset of a then b is a subset of a. Proof what would you do to make you feel like someone The element y will be a part of b. The element will be y which will be part of b. while solving while doing while doing while doing While doing it, I will tell you how to do it, you will get the proof. Make sure that y is also a part of your a then someone element which is also a part of B element a is also a part of b means all of b element a contains all elements of b is in a if all elements of b are in a means B is a subset of a I understood how to prove it, I understood it boss how to proof okay so just if a b b is a subset of a means Is a and b equal to I once again Let me repeat what to do if you have two One should be asked to prove that the sets are equal. I will show you the question, it will definitely come, what should I do? Prove that a is a subset of b and b is a How will you do a subset proof? Take x which is in a and prove that it is in b also in a means x is also in a also in b means a is a subset of b such that there is an element y that is also in b Prove that it is also in a means b is a subset of a what is understood Let's go ahead and keep looking at it again and again. I am sure the audio is playing and touch it again It will happen, so what are you saying next? Brother, something like this is given that a or b a Prove that the intersection of a and b is equal to = b means we have to make two sets equal Two sets have to be made equal Two sets have to be made equal We have to apply the same logic that a is equal to b subset a and b is a subset of a Remember, this means your There should be a cloud in the mind that Boss A should tell B and B is a subset of A Now pay attention to how you will prove it. okay give it quickly okay so brother I What is considered the same thing if A is considered a subset of B? I have to prove it, see how I will do it. Let x be any element in A. Okay, now think and tell me how much you have in common Sense read if any element in A If so, this implies that he is a Also in B If any element is in the set A then That element a will also be in uni b because a union b contains all subsets of a and b There are elements Yes, it is fine but because given in the question that a and b sets are intersections of b sets equals so your x is an intersection It will happen in B also, think about it, it is divided Why are a and b a intersection of b is equal to Now think of an element if a Intersection B contains any element if A Intersection is in B, which means it is also in A. It will happen in B also, why brother, if someone The element is in the intersection of two sets Meaning and is common in both sets meaning and in both sets so what does this mean means x is in A and x is in B Look, I assumed that was in A.A. My R is also in a B so just there four A is a subset of B you have This thing has been proved, you can prove it in the first equation Tell me I understand, now believe it. Suppose if you have to prove B.E.A. subset of a so what to do is let that lie There must be some element which is in the set B. Now if any element y is in the set B This simply means that y is your a or b It will also happen brother if any element is in b then If a or b then all of a and all of b elements means y element is your a This will happen in b also but what in the question Given that a y b a is the intersection of b equals so y your a intersection b in too Now if y is in the intersection of the two sets is the common part of the two sets, meaning y is your means y your in a also and y your There is a boss in B too, so what did I assume? Your Kiva is in B, look your Kiva has come is in A means B is a subset of A gone be e subset of a okay you call it The second equation is just from and to you What people can say from From one and two what can you guys say that A is a subset of B → A → A Barab You have to do this in a sensible manner. This question can be asked to you friends. Let's move on to three more questions. The proofing ones, then we, in the end, We will see questions related to Venn diagram. Some very good questions above. Come on, please move aside. Thank you so much here now. Also see the question, read it carefully, let's b c b three sets a b c are sets a y b is equal to a if c is given by a Intersection b equals intersection c Proof is given what to do that b equals c do proof what did you ask b to do equal c what's on your mind It will shine in your mind, it will shine If two sets are to be made equal, then B must subset C to be a subset of B on There is a problem here, you have B and C. One is to prove a subset of the other but here But a is also coming somewhere or the other, so now that Don't do it with the method I told you. If both of these are considered subsets of each other What needs to be done should come to mind but Because here with a and sorry b and c If there is also A, you will not be able to do that I told you what to do next, which I You'll think hey your brain How did I come friends, it will come through practice You just watch these things and learn them. Just pay attention, okay, so what do you do? given to you given to you given to you is the boss that a y b is equal to a y c okay you're given that a y b is equal to a y c k understood what I wrote now listen What do I have to say, whatever two sets You have to equalize pick a set b b Take the intersection of a here and b Take the intersection here as well, it's like that Multiply two by two on both sides Multiply both sides of three by two c's Talking about intersection of c with Take and take the intersection of c with That's it, you will see the answer now. Solve then distributors b The intersection with a will be your B. Intersection a then b intersection b b Intersection B and your union bus in between Keep solving and you will get your answer. Intersection a b Intersection a and b intersection C okay and in the middle your union okay friends b inter section a You can also write a intersection b as Why did you write this as a intersection b I'll tell you right now okay good B intersection B. What is the intersection of two bean sets? Once that is set then it is yours. Intersection A Yay Yours Came Union B I understood the intersection, now tell me. Small set, big set, smaller than brother B. If the intersection point is smaller than B, then it will be intersection so small set big set sorry small set big set small set big set What will happen to the union, brother, always a big set b and what's coming here your b intersection a to here you a intersection You could have written b, okay, so this is your answer. Friends a intersection b y b intersection c So b sed your something like this is coming leave it Can't do anything beyond this Look there, the intersection of c with the intersection of C with B and this What is your union here? Intersection with A and Intersection of C your union tax with and between C Solve then C intersection A write or A intersection C is the same thing here Write Union B Intersection C or C Intersection is also the same thing. Okay, now look here, C intersection. Intersection c is the same thing as union two beans The intersection of the sets c will be the right side See, the union of big and small is always there. The big one will come here. Your a intersection c union b intersection c Now notice that b is equal to is set equal to this look there are some beans Is b intersection c b intersection c Union Union a Intersection C a Intersection B a Intersection C a Intersection B friends a Intersection C a intersection is equal to b then instead of this just I understand that in the last a intersection b was written What am I doing and this is your thing in the union B intersection C this is equal to your C now You focus on the value of C and the value of B. The value of is the same as the value of C If there is value then what are you doing directly here? You can write from one and two from prime one and two which is the value of b is the same as c is the value of b equal to c prime one and two Did you understand what your B is equal to? I am clear how I am talking I will get you another similar question, don't load it. take let's see let's see okay this Look what the late A&BB stars are saying So what is given by the sets A and B? Intersection a b equals intersection a is given and what is given a y x b y equals good shot a equals b again Look, I will give you the same question. The sets have to be made equal but these two sets So what if you are also given an axe along with it? I'll do the same thing I just made you do What has been given to you, everyone please do it That is, you are given x equals b y X K B i.e. X K okay a y x equals equals b y x what did you do whatever set have to equal the intersection of a over here Both sides taken okay and here's B Intersection B on both sides So, how much is the intersection of a? got a intersection a a intersection x How much has gone an intersection x it's like this came and the union in the middle look here a a intersection went in so a intersection b and this is your a to x okay and in the middle your If the union does the same thing here too then b intersection went in so b insion a and this Your b to x is understandable and in the middle Your union is equal to the intersection so intersection b and this is your b intersection x And this is your union. Now look at a intersection x and b intersection x The value of f then a intersection a your a It is a union, instead of this you wrote 'ph' You don't know anything about a intersection b know union a intersection x your 5 so This is your f okay b intersection a I don't know So let b be the intersection of y. union b intersection x friends this is also you f equals b intersection bb Union friends, this is your understanding equal to F. I am coming what am I doing friends small Bada ka union is always bada toy achha here But look at the union of small and big The unit is always larger, so this is your A. intersection is coming equal to b okay look here carefully okay little one sorry little one big small big Always always bigger is equal to okay Union of small and big is always big, now the focus Whatever B set is coming, the same A set is coming. Whatever B set is coming, the same A set is coming Value of b is a intersection b say b Intersection a bolo one is the same thing and The value of B is also the same as the value of A. It is the same, right? From one and two, it is the same thing. What from one and to a and b you equal This is how you can do it, it's clear. Let's go over one last proofing question and What will we do after that, Boss Wayne? What are some great questions on diagrams? bola find sets a b and c true that a Intersection b b intersection c and these mt question means it is a wrong question and a The intersection c is also given, now it is easy Read the question first and try to understand it. What are you saying B A. Take out the set B. Take out the set C. Take out the set Well, they are asking to remove these sets and said what is an intersection BB Intersection C and A Intersection C Non MT is Non MT means not MT There is no empty element in these What else would it say that A intersects B Intersection C is empty, good means you You have to find A, find B and find C. What condition are you imposing that a intersection b b intersection c a intersection these two two should not be empty as empty Should not be means non-empty to be I want to understand boss and what is one more condition put that a intersection b intersection Your Fa means if the intersection of the three If yes, then Fa should come I don't understand, I'll tell you as if I took a 1 2 understand carefully Well, there could be many such examples. but suppose I took a 1 2 now Because a intersection b is not empty Should mean that there is something common between a and b So suppose I take one common thing between a and b. Li as if you can also take two but as if a and In B I took one common and in this I took three, I think it's okay. So A and B have one common one in A and B It is common, okay now listen, now you have to take it in such a way that B and C also have something in common and A and C There should be something common between B and C There should be something common between A and C and There should be nothing common among the three. Let me explain, friends, understand that I am A and C. I see If I had taken one in C earlier, The problem is that one will come out of all three. And all three should not have the same thing. No no, you will have to take two, if you understand then one and Two common ones came in C which are not here It's okay, but there's something in B and C too. If it should be common then the forest cannot take away the forest. So why can't I take it, one of the three You will be saved, understand what to do and this is yours. The answer is there, you check it, you check all three. There is nothing in common between these two One thing is common between these two There are three common in these two and two common in these two. I understand this is your I understood how to do the answer correctly. Hey, it's divided, sir, come, let's move ahead. Let's move on and let's go now friends to some forest On the best questions with diagrams and then We will finish the class. I will give it to you, okay, you will see it very carefully, right? I will also answer these questions with the help of Venn diagram. I will teach you if there is any other method, I will teach you from that also. I will teach you some other method from him also at the end Very basic question of the day, some left. Interesting and wonderful question, please pay attention Please tell me what these people are saying in school. There are 20 teachers in a school where there are 20 teachers. There are teachers who teach maths and chemistry. Well, there is a school where there are 20 teachers. Teaching maths and chemistry is fine. Okay, not good, one second, 20 teachers. Maths and Chemistry, so what else does it mean? It happened brother and means union, you understand. went that in n maths union chemistry your 20 teachers are out of them 12 teach math Okay, how many people are teaching maths, boss? 12 people now what is the confusion here to children that they think that only maths There are 12 people teaching only maths. There are 12 people teaching, did they do this? Said that only those who teach maths There are 12 people teaching maths, no He simply said that those who teach maths There are 12 people, now I will tell you that brother 12 There are people who teach maths, it is possible that among them He might also be teaching chemistry. Isn't it brother, it is definitely possible to have a question According to the calculation, these 12 people are such who are good at maths. teaches but it does not mean that it is 12 They only teach maths, did you understand anything else? Bola Pore Teach Both Math and Chemistry Four There are people who are good at maths and chemistry. Math Intersection Chemistry Teaches Four People like this How Many Teach Only Chemistry How many people teach only chemistry? chemistry teacher How many understand what from here, why understand what I will show you a diagram so you can understand it. Coming soon is just a maths union chemistry equals a maths plus n chemistry Plus a Math Intersection Chemistry Now Here This can come out of yours, please take it out. So this 20 is given to you, this is given to you 12 is given, you have to take it out It's not meant to be removed, but it will come out. You have given four so 12 is good. There is a minus, isn't it friends? This is a minus. okay this is minus okay so this is minus f So 12 - 4 8 eight went there 12 friends Now these are the 12 who teach chemistry. 12 chemistry teachers have come Only the 12 who taught chemistry did not come. How will those who teach only chemistry come? Guruji, I will only teach you chemistry. Teaching means chemistry Remove maths, remove maths from chemistry How to differentiate between sets of chemistry and math Remove the minus tax from those teaching chemistry. Two people who are both teaching Chemistry and Maths mean C intersection A And you would have a very important formula. what I just taught you is that n n s - m what will happen who only teaches chemistry and that's it your answer Okay, now let's look at this once again in a Venn diagram. Now let's look at this in a Venn diagram. Try to understand what you are saying Friends in the question, believe it is yours This maths teacher teaches chemistry So maths and chemistry friends this What happens to people who are teaching both? There are four such people What happens is only people who What is this, just teaching maths? People who are teaching chemistry, then Only people who are teaching chemistry That's eight, how many people teach only maths? Brother, look, this is your entire maths. There are 12 people teaching, four out of 12 Give a minus to those who are also teaching chemistry. If you are with maths then your only maths Eight teachers will also come and this will be completed. What does this whole thing add up to, your friends? It happens what what a union b mean Math Union Chemistry 8 P 8 16 P 4 20 and 20 such people were in the union If you could even see me, I was just fat. I want to make you understand that this is your Only Maths Meaning this is your only maths or your only Chemistry Okay boss and you both mean maths Intersection Chemistry Okay boss, let's go ahead, let's go to the next page. very easy Just focus and pay attention to what you say. are asking questions, saying that there are 200 individuals with Bhaiya there are 200 people with skin disorder, they have some 120 people have no skin disorder 120 people were exposed, 30 to chemical C1 I understand from the exposed chemical C2 Boss is saying that chemical c1 is 200 not 120 People exposed to chemical C2 30 people were exposed, maybe not 50 people okay well what does that mean chemical 50 people have been exposed to C2, which means It is not that he is not exposed to chemical c1 These are the people who might have been affected by chemical C2. have been exposed, is it written somewhere that It did not happen only with chemical C2, what did you say 32 Both chemicals c1 and c2 30 people are like this 30 There are people who are exposed to both chemical c1 Exposed what did he say find the number of Individuals exposed to f exposed to exposed to This f is written wrongly, chemical c1 and chemical What does chemical c1 and chemical c2 mean? I have to remove nc1 or c2, okay so The formula can be derived from here very easily. You guys know chemical c1 but not chemical c2 then chemical c1 be chemical chemical c1 be But if c2 is not there then minus it and you get Its formula is well known. what is the formula bro nc1 nc1 - n intersection c2 from c1 okay and what is this Here you can calculate the value of nc2 - c1 using the formula You will do it very easily, I am not following the formula. I will do it for you using a Venn diagram. Now things are alright I made it Venn diagram, okay boss, please pay attention. made one diagram okay boss okay sir now pay attention okay this chemical c1 this chemical c2 okay good friends there are 120 people like this There are 120 people who were exposed to chemical C1. Now such people are also coming to this chemical C1. If in c2 then first find the intersection You have been given 30, this is 30 given to you I understand this is given to you this 30 okay from chemical c1 these whole from chemical c1 120 People exposed are 1220 minus 30. If you give it to 90 of your friends, such people will come. who is exposed only to chemical c1 only How will those with chemical c2 come from chemical c2 50 people are exposed, subtract that like this two which is also from c1 so minus 30 Friends, this will be your 20, okay? You automatically got all the answers that Friends, your answer is done, c1 only c1 90 So just by c2 20 and c1 or c2 formula You can take out everything c1 and c2 friends It gets added to this, okay 90 + 30 120 + 20 friends 140 Understood how to do this from the One Diagram have to do Boss, I understand things. Sure, let's go brother Let's move ahead, just for the last few questions funny questions watch fun What will come, read it carefully in the question Do it in a class of 35 students 17 Have Taken in a Class of Students Come on brother, I am understanding mathematics. Is there 17 in a class of 35 students? People have opted Mathematics 10 have Taken Mathematics but not Economics but not Economics, there are 10 people who I have taken Maths but Economics means Maths Minus Economics okay good find the number of students who have taken both mathematics and economics so both taking meaning Maths Intersection How much will the economics be asked and the number of students who have taken Economics But Not Mathematics, which have taken Economics But not mathematics liao okay if it is given that each Student is taken with Mathematics and Economics is very important now? It is given that each student Neither Mathematics nor Economics Every student has already taken something, I mean You understand what it means if there are no 35 students. that every student means Maths Union Economics has given you 35, what a thing. If you understand it, you can do it with the formula. Yes boss, you can do it very easily with the formula. Look at it from the Venn diagram, it would be a little easier. Make maths, make echo, make echo, make echo Now pay attention to your math or your Echo is fine so maths teaching sessions Sorry, there are 17 people taking maths, that means Your 17 is fine, in this 17 there is only maths Only Maths Only Maths Your 10 Given Okay, and it was a full 17, you understand. It's all yours, but out of that, this is yours. If 10 comes then your remaining seven will come. Your seven will come, understood, now look at 10 + 7 This part is just the echo part. How much should come together if 35 unions then 35 I subtract 17 and it becomes 18, I have all the answers. Friends All the answers came that not only this, but both There are seven people who teach, but they are not teaching. There are seven takers and only Economics There are 18 people taking this, this is yours I understood the answer boss, it is clear, I can understand it. All the things, let's move ahead brother, great What is the question, please divide it into questions. Pay attention in a town of 10,000 families 10000 people ki family hai it was fund 40 par Family Buy Newspaper Good Diagram We will do it, what are our people saying, 10000 Family buying newspaper A at 40 So in a family of 10,000 people, there are 40 Families Newspaper is a buy at 40 How much is it friends, 10000 is 4000 If yes, then buy 4000 newspapers % Ba Newspaper Even then, 2000 people buy newspapers for Rs. 20. There are families by newspaper on end 10 C Newspaper C Friends 100% i.e. 1000 Families are buying 5 but families buy a Families A & B Meaning on A&B 5 Intersection of both A & B Newspapers How many families buy newspapers? If you do Hajj for 5 then you will do it for 10000 rupees. It happens that 5 for 5, how do you take out 500? 5 per off 10000 so 5 by 100 in 10000 tax Okay to take it now watch 3 on Ba B&C Meaning at 3 i.e. B intersection C to buy 300 people on 3 means there are 300 people on 3 People buy A and C at Rs 10,000 and Rs 4 How many people are buying A&C brother? 4 But that means 400 people and 2 families by All Three Both A and B are buying newspapers. I am buying it, I am buying it too brother. How many people are there on 2, that is, 200 People okay what did you say find the number of Families witch by a only be only three also No, not three, now for this, friends, one I will give you the formula but without the formula that we will do it as per your wish formula Well, since the formula is in NCERT, one I'll tell you once, okay, look here. You know the formula for n a y b It happens n + n b - n intersection b gives you this Do you know the formula for two sets? It is like this. There is also a formula for three sets what is a y b y c a y b c a Tax take n b do n s do minus a minus b intersection with this This gives b minus the elements of intersection c Do this to form an intersection of the elements of c and plus do n n a intersection b intersection C okay so this formula note Do it evenly, I will give it to you with this formula I will not get it done, however if you want this formula You can do the rest with this formula also. I'll get you started with a Venn diagram, okay? Okay, so what if everyone focuses on it? He was saying that it is good to divide it into questions. Now see what he said to us, take out only A Meaning, how many people buy only A newspaper? If there were families, a newspaper was made. b made a newspaper and c made a newspaper Now focus on what I am saying first, this is your The person who buys the newspaper is the one who buys it. or buy C Now answer some questions quickly. Then you will understand Venn diagrams better. I'll come okay guys what is this What does this circle represent? Representing families who are She is buying newspapers but there are also such Look, there are families who buy whatever B and C also. Are you understanding what is happening between B and C is also buying it. Okay, now some questions. what will I do what is this This is the part of a family which only How can I buy A and not buy only A, B and C? I understood brother, this part B and C. I am not coming in, you see B in the circle C This part is not coming in the sphere. Also, this part does not fit in circles A and B. What I mean is that there are such families who only She is buying so much of this yellow newspaper. Part is not coming in B, A or C I am coming, meaning this is a family which only B is buying it, can anyone tell me this? what is this part this one Part Y what is this that A are also buying And B is also buying which A is also buying Yes, B is also buying it and some of them are also like this Whatever you are buying, tell me if you understood it. What will happen, tell me what will happen to these people Yes, there are people who are buying this too. C is also buying and some of them are also buying B. I am buying it, I understood it, it is clear Okay, what will this be? This part is like this. There are people who are buying all three ABCs, okay? Now try to understand what I am telling you I'm going okay friends you 200 people are given who will buy all three Meaning the value of this thing is 200 for you. If the buyer buys 200 then this value is your 200 now tell me what is the price of this thing Buy B & C as given in the question How many people are there who are going to buy B & C? Sorry, there are 500 people who bought A & B. This is 500. Subtract 200 from 500 and you are left with 500. 300 left 300 friends this part is yours 300 will come what is this 300 which is A and B I am buying c I am not buying you understand yes, which is this part, which is this part This is common only in a and b, meaning this There are people who are buying both a and b I understand, tell me like this. what is this brother a intersection c a intersection c is 400 people, among these 400 people Subtract 200 from this and you will get 200, which means this is 200. There are people who are only studying a and c or a and c are buying b is not buying look No, you see, this part is b It is not coming in, it is coming only in a and c Similarly, friends, this part Your b intersection is going to be c's b intersection c Yes, a is also included in it but b Intersection c is 300 so this is 200 out of 300 Subtract the remaining 100, this 100 is yours. be a part I will understand, now friends see the complete a How much was the whole a 4000 people are going to buy So 300 500 700 minus 4000 is 3300 There are people who are buying only A newspapers. Okay, how many people are there from B, brother B? If you have 2000 then 300 500 600 out of 2000 Two 1400 people are buying just such B How many just C ones just total C your 1000 Out of 1000, 500 are gone friends, 500 people are C just buying I understand the logic, so just buy A only A 3300 people who bought Only B 1400 People none of A B and C means not all three All three are buying, brother, they are not buying. If all three are not buying then how many such If people are not buying all three then this Let us find out who the three buyers are How many people means everything is yours I think 3300 this is your 4000 5400 5 5 6000 will come, okay, so basically your A A Union B Union C all three are buying How many people are there like this, you are 6000 people. Okay, those who are not buying anything, which ones? What will you subtract from 10000? Given that you subtract 6000 from 10000 If you give and you have Rs. 4000 left then this is your friends non 4000 buyers You must have understood from the diagram, right? The question is being cleared in a proper manner Let's move on brother, good question. You will enjoy the questions a lot. Very very interesting question Okay, just pay attention to these. Survey of 25 students it was found that 15 Had taken Mathematics now I am Direct I will do this using a Venn diagram, direct Venn. okay from the diagram pay attention anything There's no need to write it down, okay? I made this circle, I made this circle and this Those people are talking about three sets of circles. You should look carefully, okay, so 15 people Mathematics Ltd. Okay, so this is your Mathematics bolo 12 ne aapka physics toy Your Physics Tell Me P11 Your Chemistry, tell me your chemistry So let's talk about math fix chemistry. It's okay, just pay attention, right? 12 People have taken maths and physics, right? So here I write my A P A P. 12 okay 15 mathematics so n a your 15 Okay, now notice one thing, if maths Just because there are 15 takers, it doesn't mean that There are only 15 people taking Maths, which means this is the whole Your part is 15 in total, I hope you like this. I understand, I will copy it as well. I will give it to him through another method. I will tell you so that there is no confusion. If there is anything left, please pay attention, okay 11 hai tekan chemistry hai na to n s your 11 yes you understand this okay five has taken mathematics and chemistry and Meaning intersection means maths and chemistry There are five people taking both, so you can here You can ask me to take Maths and Chemistry There are five people okay nine had taken Mathematics and Physics to Nine people who took Mathematics and Physics okay four had taken physics and Chemistry to Physics and Chemistry Brother, how many people are there to take it? There are four people. Okay now look ahead there are three taken all the three These subjects have become very easy. I have taken Maths as well, Boss, I have taken Physics as well. You have three people who have also taken chemistry. Okay, now let's first this one. Now let's see how we do it directly using the diagram. Okay, all three brothers who are going to take it, these three Representing the trio taking three People have written three here, now pay attention. okay to give what is this friends what is this There are people who have taken Maths and Physics I have taken both because this is the part This is happening in maths as well as physics. Guruji, this is coming in chemistry also. Friends, there is no load on coming The common part between maths and physics is This is the only one if you pay attention. Okay, so let me talk about maths and physics. Where is it written to take Maths and Physics? There are nine people with any error in the data. No, right, nine taken mathematics, yes, okay. So this is your nine. Three out of n is six left, so this is six Gaya means what are these six, these are six such people Those who have taken Maths as well as Physics I have taken it but I did not take chemistry because This part comes only in Maths Physics. I am not able to get into chemistry anymore. Look how many people are taking Maths and Chemistry. People are boss taking maths and chemistry If there are five people then these three out of five Gaya do bacha so who are these two people who Took only Maths and Chemistry, Physics Did not take Physics and Chemistry How many people are there with Boss Physics and Chemistry students are given Four people, two out of four went one I understood the rest for sure, now look here only How will I come to take Chemistry? If there are 11 people then two out of 11 are sitting one after the other. minus 11, only five left Five people with chemistry, I just enjoyed it. What will happen to the maths students? The maths students are 15 So 6 + 3 is 9 2 11 15 divided by 11 4 Only four people who took Maths were left. 6 for Physics + 3 for Physics 9 for 10 Physics You had 12, so this is your only two left. Now answer two questions for Physics. Two brothers are going to take only chemistry. Your five people only take math mathematics Four people taking only Physics, two people taking only Physics People Physics and Chemistry But Not I have taken Mathematics and Physics. I have taken Chemistry but not Mathematics. I took this part, look, this is such a part Which is coming in Physics, Chemistry I am coming into the realm of mathematics If it is not coming then this is your forest. I understood mathematics and physics but not I have taken Chemistry and Mathematics. I took Physics but not Chemistry. So this part is yours friends, six Gaya six people are such only one of the Subjects: Take only one subject There is only one subject, so four people are like this There are two people who have taken only maths. who have taken only Physics and five Such people who only understand chemistry All four took one subject, these two took one All five took one subject How much is it 5 4 9 2 11 so this is your 11 Come Gone okay okay sir at least one of the three Subjects mean I have taken something or the other. I have not taken anything at least one one means I have taken either one subject or two. If you have taken either subject or all the three subjects Brother, just add this completely and you will get how much. 4 plus 6 10 plus 3 13 15 17 18 and plus 23 When I went there, there were 23 people who took something or the other. If you have kept none of the subject then brother 25 23 people have taken something or the other from the student. Two survivors who took nothing I got it, okay, now you can give it another try. How could I do you good This is not copied, should I copy it? wait okay don't do it that way If you want, you can do it, I'll show you you that Method copy oh it's copied twice come on Look carefully, okay, now I'll erase it. I am telling you this thing and one question. I will give it to you at home, just take care of it. You could also do what you do Make equations, call this A, call this B Say it C Say it D Say it E This is A and this is G, okay, one by one. I will show you, right? Come on, pay attention, right? Meaning only Maths B means Maths Physics But not chemistry, I mean only physics. You understood it is clear, you can do it by making an equation also. I can show you one Neither this one nor any other one. Let me show you, okay, let's say this question This is your last question of today's class. Okay guys, last question of the day. Finally, once I see it, Is the recording going on or not brother? The recording is going on at full speed, someone is on top No problem, what are you saying now, college? Awarded 38 medals in football 15 in Basketball and 22 cricket is college Boss is a college Boss they have medals They should award medals, okay? I play football, basketball and Very good in cricket now pay attention or take your football or your basketball Cricket is fine if the medals are a total of 58 Men and only three men got medals in all the Three sports, three medals, three people like this Who got medals in all three sports? Okay, if these medals went to a total of 58 Men 58 Men have won total medals Meaning union is given, basically how many Received medals in exactly two of the three Sports is looking difficult, what did I do? I used my brain, I I I I only won medals in football. The one who met me said A to this one and B to this one and C to this one. This one D This one E This one A This one G Now watch If you pay attention, football has got 38 medals. Meaning a p b p e p d understanding a p b p e I You are given 38 15 basketballs Then B p c p f p e b p c p f p how much is it brother 15 okay If there is cricket then d + e + f + g d + e + f + g how much is it brother 20 now if you focus here If you do it, it has been given to you brother. Look at you, here we see three men Got medals in all means e you three It's okay, let's see what happens next. They are saying that 58 men got medals. Meaning, these are all those who got medals. Yes, brother, I have given you a PS b ps c ps d ps e ps a ps you Given 58, do you understand that have you given something like this what did you say how many Received medals in eighty-two of the three Sports Bus Pa Minute How Many Receive Medals in at least two of the three sports Think about what this means Tell me how many people are there who only Medals were won in only two sports, friends. b is a person who has the part b Neither did he get a chance in football nor in basketball. I also got it, look, this part This is not coming in C, meaning this is such a part which is coming in two things then you have to b have to be taken out okay and and and similarly D also and also have to find f because Because BD and A BD and F here I I will also color this bd for you guys. And there are people who just Medals have been won in exactly two sports B in football and D in basketball Wale likes softball and a football and a cricket Those with I and F like cricket and basketball So basically what do you have to find out? To find you To find b + d + f I understood, okay, I will tell you how to do it now. I used my brain to find out how b+d+f If I do these three plus meditation Notice if I add these three equations Let's do the addition and see what comes out, 1 + 2 = 3 what will come okay so look twice b is two times d is twice a is three times e is okay then twice b twice d twice f three bar e and a c and g left a c and g left and What will the right hand side become? 38 + 20 = 58 plus 5 63 this is your 73 now pay attention times e so this is your 3 3 * 3 9 9 gone there So this is your 60 4, how much will it be 2b + 2d + 2f + a + c + g Now we get a Now we get bdA If the work is about age then age is not important. Take out the value from here, did you understand what I said? a + c + d see a + c + d so Big f went there so 58 - b - d - f and mine e 58 - e becomes 58 - 3 55 Friends, this will be your 55, this will be your 55 - B - d - f I have come, I understand what I have done I mean BDA, I mean it BDA should find out the age from here Now keep the value edge and this is it. Your 2b, here comes your 2d, here comes your Replacing 2f and edge by 55 - b - d - f = 64 So, if we solve 2b - b, friends, b will become 2d. - d friends plus d will come to 2f - f Friends, this will become your F, see it will become a big F. Your 55 went there, so 64 of my 55 went there. I think your answer is correct 4 more 5 is 55, isn't it 55 minus yes, this is yours. It is okay, so there are no people who Friends medal in exactly two sports found Okay, so finally our chapter. It ends here, don't try it. No, let it be okay Just try this, I have answered as many questions as possible. I have given you my thoughts in between sessions. Roughly three or four questions only Yes, please complete it and comment. Please tell me the answer in the box. As you all know about the last one I had to re-record an hour and a half. Because there was an issue with the mic, but I hope The mic is working right now, yes it is working, okay So thank you so much everybody And as I promised, I will Make sure friends, you have to put in your life and sweat. Get out butt best one short lecture on youtube1 I am promising you this about maths, okay? Is there any complaint, any problem, any trouble? I have to do some additions, some subtitles from my side. I want to do something from my side, please let me know. Tell me in the comment box, okay? I will see you guys in the next lecture. Next week that is relations and functions Till then take care of yourselves Have fun, chill, do what you want to do. Please tell me anything, any edition, any sub what did you like what did you dislike okay can we do anything else okay I did everything but no need to do it okay these notes Please make it neatly in your copy. You should have notes that brother sets Wrote the chapter and wrote every question in it It has happened, how to do all this It is written Everything Everything after this Whatever you do from your side, any 11th class Are you using any book? If you ask questions, you will get questions but Your main focus should be on my notes Questions: Your NCERT questions are correct. Let's thank you so much, everybody, love you all Tata Bye Bye and Take Care Bye Bye