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 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 This chapter is from your class 11th and many more. I think the children might One short lecture of the chapter is about to be received It's too early, isn't it? Let's start. 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 Okay, let's quickly focus on these hours. mathematical language everything in this This is a TV, this is an AC. Defined if we can definitely say weather a Word Collection of Collection of Well Defined Speak Collection of Collection of the Most 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 What is a Form Set Builder Form? well we talk about I will give you an example of the roster form. off multiple of 50 multiple of 50 off Exactly how a set will represent This collection A collection of all multiples of So this is one Infinity Mano and how did you write set A bhaiya x is Natural Number less 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 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 or greater and 10 or less It is clear that what I mean to say is just this If I give you something you x = 2n ok brother means it is a multiple of two Now I have to enter integer, so how many integers 2 * -2 -4 next which is -1 then 2 * -1 -2 Which row is next? If you understand the logic this much. what age is that n 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 would have given you a set a I told you x is true, that x is - 5x + 6x How will he know the quadratic Solve the equation, what is x brother, this is x You can write x s - 2x - 3x + 6 equals 0 So x common x-2 -3 common x-2 equals 0. This is your You took the common x - 3 = 0 so x is your 2 3 Meaning, if you put it in roster form If you write, which ones are in set A? Now you understand because it has two elements. What do I say if there are two objects? because not an object or an element that belongs, that belongs, set Infighting 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, okay 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 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? means non MT means set your MT Must not be fi set null set void set There should not be any element in it I took 2 5 6 4 Set B I took Brother, give it 1 or 2 I came in R Equivalent Equi be equal such that these two equivalent sets The builder form is given in the first one very 2 3 4 5 6 78 Will it come or not, understand 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 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 Whose better word is it, so better word is it Just write the letters separately. 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 You leave now Builder Form Set Roster from Builder Form If I were in your place, I would ask this question I know how to do the roster form but The Set Builder form is slightly different from the Roster form. I would have given that if I had been given something like this then I This this this this is very nice what are you saying is equal to 3an where a1 gives you This is your infinite number because natural numbers are never 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 What is the answer, what is the answer, Karli 3 3 means no after that 27 dot dot dot dot Brother 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 MT is set okay what does that mean 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 let us know these 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 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 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? 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 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 then 4 so these are the six values ​​of n out of which Excellent 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 So what you would simply write is f is not a subset of b You can write it like this f is not a will be present in What are the subsets of any set? anyone or anyone and you also get a formula It will be okay 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 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 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 subset mean okay let's It is proper to listen very carefully subset okay proper subset means if Do you know that total subsets will be formed from this? F will be one, O will be three in the set will be t will be 2 3 be and what else and 1 2 3 would be okay so one Similarly, the set is proper. you write like this Suppose set A Of 10 ok There will be number of 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 2 to the power 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. Power th will become 2 to power 6 means How much more than 8 8 is 64 56 more How many subsets are more? Understand how many 56 are more. But one small thing is something to understand. subsets of r okay now first you have a Let me tell you something, is everyone understanding this? that natural numbers are a subset of whole numbers Wali number is a subset of whole number because any number All the numbers here are here so this 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 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 had forgotten this, let me tell you now. Look like you know that b is a subset of a is a subset of A I understand e is also your is a subset of A okay now understand B is your a Is it a superset of your B? power set like I took a set okay I took the basics, the basics, 1 2 3, okay. Power set of a, what does it mean? 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 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 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 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 There are two elements here, one A set is created with both elements. I will ask you a lot of questions about this. A set is given which contains two elements The second subset will be whatever element is there 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? 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 No, yes, if it were like that, there would be a What is the easiest number of subsets to be the Boss number? I will only understand, I understand, now what? Set of a your one a What 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. Zero then 49 then 98 then 147 and so on 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 5 kept okay so 49 5 - 1 4 so friends this 196 49 4 49 36 16 There are things coming in which by consuming you All of them must be in your Y. Ekas inva there four x is a subset of X is a subset divisors of 68 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 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 Rectangle will show you the universal set Universal set okay now because a and b If you do, then friends, what is the meaning of union? Union means and is 2 3 4 5 If I ask you a uni b This means elements that are in a and b I give all 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 - aye 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 So okay, what does disjoint set mean? Yes, just learn that, pay attention, this is okay If this is your fee, it will come, then this is what we call it. pay attention to this I understand what you are trying to say Okay, so what are some basic questions first? Compliant a compliant 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 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 I will have common eight, 10, 12, basically all of them. Elements I understood brother, think for yourself and see everything here. Natural numbers are all natural numbers here 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 If so, this intersection will be yours. 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. Intersection b is coming, do you understand this? What happens friends, you just have to understand that 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 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 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 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 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? 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 of Would Compleños is it okay to do what are you saying question I Dr This Bee Ka Compliant a y b excluding Compliant here neither Compliant 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 am trying to explain. 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 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 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 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 which is not present in B and is present in B There is no diagram, come brother, yes it's okay. 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. 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 Friends, a my b is done, from here you It will be very easy, very easy, very easy, just like that Pay attention to what will happen with B minus pay attention pay attention pay attention okay So this is your b-a, this much part of yours b - a and friends what do you call this - a will also be called only b, only b What is the common part of a and b? 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. 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 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 number of elements in b minus number of First, let's consider what he is saying. that number of elements in a 17 is the number of Elements in 23 is the number of elements in is the number of elements in a plus the number of 40 So this is your arrival 38 This is your arrival 40 How many elements are common in only and Meaning these 21 elements which are present in a Exactly tell 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, 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 are you basically being told? Universal Set Your 400 Across the Universe Some people also speak English. 200 people speak English meaning maybe And you say okay how many can speak 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 You have to find out what you want to remove. Now attention will be equal to n These are your 200 people. Went Speaking English too 50 people who also speak English PS 150 400 Look at the intersection, you can see this I was as if n Compliant Friends, if there are different complaint sections Do and Compliant of any thing A y B means 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 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 It used to be childhood what are you doing here a y b 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 * Intersection c between union understood easy Hole of Union Compliant section hole 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. I will get you all done today There is a possibility, so what are you saying? and b have three and six elements That means how many elements are there in it, it is three. How many elements are the cardinal of the set b? least and most least and Maximum means minimum and maximum Put the first one, okay friends. Maximum Maximum A Intersection B B Okay friends, talk about the minimum first. Minimum What It has six elements 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 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 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 There is nothing when both have something in common 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. It's okay to give, I made him boss Wayne This is the concept of a and b, pay attention to it. means this a means this b Compliant The region is the common region of both of them. 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 of c Compliant Intersection instead of minus and a like Compleños What Compliant B's Compliant those Compliant This b is written as intersection. Now look at b. Compliant A if 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. 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 Your a intersection b Compliant Minus instead of section Compliant wrote it after Compliant It's very easy, now look at it and solve it, tell me. Compliant Union B and your intersection inside so this Compliant of Compliant Pay your a Compliant Of From 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 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 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 means a is a subset of b such that there is an element y that is also in b Also in B a union b contains all subsets of a and b There are elements Meaning and is common in both sets meaning and means y your in a also and y your Barab You have to do this in a sensible manner. 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 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? is the boss that a y b is equal to a y c 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 Take and take the intersection of c with That's it, you will see the answer now. Intersection a then b intersection b b union okay friends b inter section a You can also write a intersection b as b y equals good shot a equals b again So what if you are also given an axe along with it? X K B i.e. X K okay a y x equals intersection went in so a intersection b and 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 It is the same, right? From one and two, it is the same thing. What Let's go over one last proofing question and What will we do after that, Boss Wayne? 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 What are you saying B Intersection C is empty, good means you two should not be empty as empty to be I see I understand this is your 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 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. 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 n s - m what will happen your answer Okay, now let's look at this once again in a Venn diagram. There are four such people Only Maths Chemistry very easy Individuals nc1 nc1 - So just by c2 20 and c1 or c2 formula You can take out everything c1 and c2 friends 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 Come on brother, I am understanding mathematics. Is there 17 in a class of 35 students? I have taken Maths but Economics means Maths Minus Maths Intersection Economics But Not But not mathematics Every student has already taken something, I mean Friends Family buying newspaper A at 40 % Ba Newspaper All Three It happens Tax If there were families, a newspaper was made. or buy C 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 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. Two 1400 people are buying just such B 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 If all three are not buying then how many such 4000 buyers 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? 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 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 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 Come you that 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 given, 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 which is coming in two things then you have to b have to be taken out okay and and and similarly D also Because BD and A BD and F here I I will also color this bd for you guys. Medals have been won in exactly two sports Wale likes softball and a football and a cricket 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 then twice b twice d twice f three found Get out butt I have to do some additions, some subtitles from my side. I want to do something from my side, please let me know. It has happened, how to do all this