SETS in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced

0:09 Hi How are you kids, son? How are you all? what is the trick for you guys tell me quickly My voice is reaching you, son. that after a long time ours is not reaching today We are meeting soon in the Manzil series tell me once if you guys can see me can you hear me? am I able to hear you I am looking good, tell me a little late OP hey brother what happened you already started taking the hat take this cap which watch are you wearing which one from Planet Key yes sir you are looking good oh wow Ok fine friend thank you friend thank you mister Thomas Shailvi is speaking

0:54 well i understand son where do you get your name from have you brought it hey cool sir yes sir you are looking smart wow it's good it's good friend i like this I started to feel that I am getting old hmm good evening all of you love you from arjuna bach love you too beta love you to love you all from all the kids wherever you are But you are also reading this as you are, one thing always take care we love you so much even if we never meet But there is a connection between us and you. And for that, son, for that, connection, we People will bring you Manzil classes so that even a single child can benefit from this can avail free of cost classes and its If the future can be created then there is nothing better than this I think it cannot be complete for anyone

1:40 Right sir please give me beauty tips in life I'll tell you two beauty tips brother, watch homemade food Eat well and sleep on time get enough sleep for six to seven hours You will always be young just like me hmm okay yes don't eat too much junk food Don't take any tension here and there live your life normal Let's do it, great, now let's talk about jokes Enough of the jokes, let's get started Look, it feels good for a while It becomes fresh when we start People talk a little funny First of all tell me how are you guys doing Study of Manzil Series How am I feeling, write to me on chat once Tell me, you might be seeing a few things, look. You have too much work sir

2:26 There is a backlog and I am unable to ask a question I have been able to theorize that one thing would be this Your second option would be that sir your number didn't come I am giving the test, I am studying but The number is not coming brother, what is the third one it will be the third one that sir now as I Sir, my exams are getting closer and my tension is increasing. Isn't it so sir, the stress is increasing a lot Sir I am unable to sleep Sir I am getting depressed I am there, you will say sir you are on our state Are you laughing or not? It means general things. I'm telling you what could happen And the fourth one can be yes sir it is going well that very few people will be the same I will write mostly to watch the kids yes bro this is what is happening No

3:14 well done yes Stress D Motivate tension only Tension yes there are two or four durations and They come to see the duration that what is the duration going to be yes good sir its going well Well done very good very good IIT I I am coming very good this should be the spirit Son, you should have full confidence like this What we have inside us is no less than anyone else It's okay, you don't have to separate yourself from anyone at all don't underestimate them and specially those kids who are somewhere Can't study or can't afford the fees could do it and yet he might think that he knows No, those people who are big are ahead of us

4:01 Going to the institute and offline there is nothing like that y'all son there is equal capability inside and this I'm not saying this just for the sake of saying it The fact is that hard work is inside you The capability to do it is more than them it is ok isn't it, to whom god gives scarcity It also gives him the motivation to work hard Always keep this in mind, isn't it? Keep being effortful, son sir, listen to the poetry Give me a new poem I created such a nice original poem for you That the one whom God gives scarcity, he has to work hard It also gives the passion to do better than this I knew it must be some original shayari you keep on writing shayari today I told you one original story, come on I will also tell you about a duplicate, then we Let's start, I understand the meaning of duplicate aren't you? Yes, look through the photo But I found it quite relevant to you guys.

4:47 so so I thought why not Let me tell you ok Brother Yes Depression is like a curd of a depressed mind Went Sir, come on, everyone will listen to a poem Specially for you, I have someone I liked it I thought that This destination is absolutely apt for you guys It's okay for the batch brother so everyone will pay attention People, I am yet to reach my real destination Look friend, I am not that type of poet I am here to forgive you after reading my rhyming song I will tell you the real destination now yet to be achieved The test of intentions is yet to come did you listen carefully to what i said just now

5:34 So the real destination is yet to be achieved, only intentions The test is still pending, it has been weighed yet A handful of land has just been weighed The earth is yet to be measured, but the sky is yet to be measured, do you understand? So what you are doing right now will make you feel Sir, he must be doing a lot of things. you are doing it exactly son butt Trust me there is still a lot left in life you will achieve so much you will achieve so much For which you will do it, just starting now So son, don't be afraid right now Don't think that sir it has just started So I'm just so tired right now I am demotivated, keep trying son Always keep trying hard in life Working people get success and they we will definitely move ahead okay brother so concentrate Everybody will take care of each other

6:21 whatever you are saying sir wow very nice sir wow yes wow wow I have done it son but now This also has to be implemented, it is not just that I heard the poetry and moved on, poetry that Do you hear how many have been implemented till date? If you listen to it, then it is a lot of poetry, aren't you? So he doesn't just want to listen to Shayari It is also okay to implement Is We Come on brother let's start now with this small thing Hope came with a motivational dose for all the children The two-four that come in the beginning

7:06 They wait for a minute and then their enthusiasm returns Today, my son, my passion has cooled down but not you have brought such a chapter today which all the children can do very easily Even if you haven't read any other specific chapter There is no problem, this is independent There is a chapter and I am telling you the question its question son four number free number Most of the time JE is inside most of the time it's just terrible bad luck If it is yours then there might be tough time in your set jaaye but most of the time its a question It comes very easy, it is a set chapter And the duration ones have come, I know the duration Many people would start writing the duration and I wrote it the same way I was going to say it Di to duration today's attempt is this brother one shot means one shot without break Let's finish it ok brother without a break means Complete the entire chapter within 3 to 4 hours Give and trust me, this is the only chapter, son even if you took three hours to do it

7:52 Infact you can find nowhere on the entire internet I won't even be available for an hour, still you I will get all these P.Y. done for four hours why there can be as many as possible whatever can be I will get almost every type of thing done for you Now the question of this is a very important thing that I I want to tell you guys about the set chapter from the point of view of that If you see this till 2022 then one of its The question was confirmed 100% i.e. guaranteed Take it, this was bound to happen in JE The question set used to come but last year They created some sets within the set I have given a question, did you understand some of the sets? I understood the question set given inside the question I think you are P Y Koo meaning in 2023 You will get less, basically many in 2022 If we meet then the chances are very high that son Because last time they covered this chapter

8:38 If you ignore him then this time son this don't ignore it and do it again son start paying attention and this time JE's You may see more questions inside Okay, so everybody should put in full effort into this. will study together with the children who have I read a little bit and then left that too Children can solve this question very easily Because the most important thing is that you are independent There is nothing special about any other chapter Put it inside if you spend three hours on it If you read it properly then one question is for sure sir There will be a function too, son, how will the set be different The chapter is function and the chapter is relation If it is a separate chapter then we cannot do set and relation we are just setting up the relation Your end function will be a separate chapter together Right Let go

9:24 Let us start brother, let's start again Everybody please write quickly and tell on chat that Sir we are absolutely ready notebooks etc pens The pencil is sitting with water and is absolutely Now we will start today with 100% focus Write down the chapter that is set quickly and tell me Once yes and those children who are studying for the first time there is no problem for them either We will run completely from the very basics I will give you the theory and those who are revising it is also good if they have one question each Yours will also go, those who are revising He must try these questions himself To We are ready Guruji ready ready well done son very good we will win sir we will break it very good like this Hey son, effort from within means belief from within. start doing it first there are a lot of kids

10:11 Are you preparing from the inside? I can't believe we can do it First, we must start by speaking the truth to ourselves. you can do it only then it will come from inside you Energy will be released to clear it This is a very important matter people You ignore what is actually yours The body will feed its mind, right? Your body will cook the recipe and that is all will try again If you think from inside, hey friend, I am doing it I don't know, maybe I won't have it, so my body your efforts will also reduce but if you Day and night the mind will keep saying no brother I can do it, if I do it then it will double The effort will come out on its own, okay let's go will start well done well done son we will start I have told you the duration will be done I think you hit the forward button son, let's go then What are we going to do today inside the set First of all we will set the basics of all the topics Let's start with the definition, what is a set

10:57 From there onwards the rapes of the set will begin There are a few ways of presentation I will definitely get NCERT things done as well Children who want to study basic NCERT Do just a few things in the beginning nuff is and types of set all definitions Operation of Sets Laws of Algebra of Sets you said de morgan law associative law If you have heard about cumulative law then all that things we will read here and then most important thing cardinal number a union b the formula that we have used in this PNC which was also used to calculate the probability etc. also use cardinal numbers The probability of union B or you can say Questions that involve Venn diagrams That is the most important thing in this There are chances that most of the questions will come And this also appears in other chapters of PNC Probability also appears in the question If you feel like it then you should get one or two done too. I will give it a little flavor brother

11:43 How are cardinal numbers used? The question has come in even advanced using cardinal numbers on it and I will show you in the last 2022 paper today You will get the Advanced question of 2022 Numeric type set based on chapter There were people who think that brother there is no set Sir, this is a chapter, will anyone read this as well? Then sir my reputation will be ruined read this Of yes you understood, it was bad to be insulted yes but it is not like that everyone has to read the set I have to read it son, it is a small chapter and in this There are a lot of question chances with carton product off set now this is one way is the bridge of sets and relations okay so we I will stop here, till the bridge, till the bridge I'll drop you across the bridge It should be done in relation and function next

12:29 Whenever the chapter comes further but till here I I will get you started in set theory Carton product is ok till off set brother And there will be plenty of PYK as well but mainly py k in the last few Difficult P Y Q in last I will get it done for you, okay brother, I understood. did you go or not understand yes let's go Son, let's concentrate now, let's start Now let's start our work, brother So first of all what is the chapter set You have heard this bookish language in many places Hogi set is a well defined collection of object is fine it's too much focus on the word A well defined collection of is done object set of books set of

13:15 Students set of notebooks kuch bhi bole We use sets a lot in general too is it so, isn't it Brother, the meaning of set is well defined Collection means whatever is inside it Objects are coming to be well defined it doesn't mean that you have done any and made a set out of that and I did some If I made any statement then everybody would say the same thing If you were able to make a set, we call it well defined ok as in example english Vowels Collection of Vowels in English Now whatever the alphabet may be, if any person If this one makes a set then that one will make a semi set that is ae i o u because these are the vowels this is the truth this is the ultimate truth that the vowels are a e i o u okay Brother, the ultimate truth is well connected

14:03 define say okay brother like sir well Give an example of which is not defined Do this collection of difficult topics in maths sir Complex Line Sar Coordinate Geometry Sir, this is the calculus of the whole world People can make different sets of this, right? Brother different sets can be made in this If someone says anything, I will say everything just for the set except I will say yes okay brother so this is a it is not set because it is well defined no not every buddy is going to give you The same answer so everyone gives the same answer That would be called well defined and whose Not everyone gives the same answer, everyone gives different answers It could be an opinion, brother, everybody has an opinion If someone says something according to his own opinion That is your set in mathematical language It won't happen, I understood it brother, yes this also happened

14:51 See a collection of good cricket players of India, now a war will break out here son is there someone will say it sir sharma someone will say it Virat Kohli will someone say thaala sir i am If I like S Dhoni then it is up to you Depends on the Australians If you ask, he will say something else, okay brother So this also will not be called a set because this well It is not defined, it is also not well defined This is a well defined set and a collection of First Five Prime Natural Numbers Ultimate The first five prime numbers are the same as every prime number in the world If you ask a person, he may tell you the wrong thing But he can't be right after being told he's wrong did you understand what it means even before 5 prime numbers are fixed Which ones are these? Don't tell me, brother, I'll cut your nose It will be yours 2 3 5 7 11 this is yours First five prime numbers Natural numbers

15:38 Right, so this is the ultimate truth, so this too It is well defined, yes, after that I am an integer squares are less than 20 now this also this also Your well is defined, which are the entities If the square of the number is less than 20 then it is this is also set this is also set of most naughty students Of Arjuna hey friend Arjuna has come come you do this you do this because ppt I have brought it from there so you can do this If the destination is fine brother then what will happen to this set of most not students sir i am Sir, will anyone say that Sir, it is me, Sir, that is him, He is not there and I am not there so this is also well it is not defined that means it is not a set Ok Brother Yes, I hope everyone understood the definition of set

16:24 You have understood, you will read it like this, see the chapter You will understand everything in a common way while having fun This is a chapter of sense, there is no much brain in it There is no need to memorize too many things If you read it this way you will understand everything It will go inside the class, okay brother, let's go So now you understand the meaning of I hope well defined Let me tell you the ultimate truth in Hindi and let it go So now you can learn the notation of some common sets. You already use it for a natural number Do you use double hole number for hole number Meaning zero also comes j jad and i jad and I means for integers then negative also comes what is in the hole number Negative does not come, natural comes from zero Son, the number comes from positive, don't cry aata z+ z+ yours is kind of positive numbers real positive integers because z is for integers and small over z If you add sa plus then it means z+

17:10 positive integers that means natural Brother, the number will become z+ now many people Sir, who gets confused between positive and zero? Do you come too, you tell me, your son If the marks are positive then will it be zero? There will never be any zero in positive It does not come, nor does it come in negative. Zero is zero brother, zero is not positive there is a part of negative in z plus positive integer z minus z minus A negative integer will not be zero and q You must have noticed that we use it in many places q q is the set of rational numbers p b y the form The numbers 2/3 7/5 8/9 are called rational 1 3 Integer Total -1 Total Total Your rational numbers are the rest Do you know the set of real numbers? the whole of the world

17:58 Let me subtract q from real in rational So sorry should I subtract the rational from the real So we will become irrational numbers i.e. √2 √3 It's all your story It's okay brother, let's move on son go ahead go ahead after that There is a representation of a set, this is basic The funda is done, what happens to the set now How do you represent your son in two ways? than we represent the first is Roster form which is also called tabular form are roster or tabular form tabular or roster ok now what does roster form mean what is basically what is done by curly brackets Look, I had written the sets here You saw there is a statement written and a it is written in curly brackets isn't it written one the statement is written in a curly bracket You saw this statement here also

18:46 it was written vowels set of vole english I had written the statement and I added it next to it I wrote AE IO or this form put a comma inside the curly bracket Whatever we have written we call it elements hain beta roster form this is called Rooster form right to set of all natural Roster form of numbers between 3 and 11 what will happen between 3 and 11 then three is four don't take three don't take four start then there are four to ten curly brackets Write all the elements with commas inside Let us call it roster form simple set of all letters in the world independence What alphabets are coming? Have you brought them? is coming N is coming D is coming E is coming yes p is coming now e is coming again and again so

19:32 I am writing this to him again and again not just once I wrote it, just wrote it once and also wrote N I wrote D also I wrote E I wrote N If there is any light left then they are coming brother they are coming If you are then this will be your set off In all the letters of the word independence which It is repeated, it is not written again and again okay just write it once for the set Someone inside keeps saying that the tooth is set So someone is writing three three three in it It makes little difference inside the set So you should remove the repeated ones and minus them. you have to give it okay it's easy and after this What is the set of all odd natural numbers odd natural numbers 1 3 5 7 9 and dot dot take it because it

20:24 write these by using infinite curly brackets Okay, yes, this is the set that is written it is called roster form let's go Now what is set builder form yes there is a set builder form There are two forms of set builder form There is a roster form, I told you first you have a roster form which Convert statement into curly brackets we speak to do in english If we put the statement inside curly brackets If we convert it then the curly brackets That roster form has come, this is the opposite thinking take it friend now you have to do it son A set is given in brackets etc. Change this to an English statement two let's say tell him tell him Your Set Builder Set Builder View Name It is understood from the set Builder Sets Builder means the one who builds the set.

21:12 who built it, who built it Look who built this and how did you know could guess that it was because this statement If it was given then we call the statement set builder form because with the help of this you built the set okay like what was this set of all odd natural so this This set has a statement written in white builder is form because with its help you if you can access this set then you can What will you say, what will be the set builder form See it right below the following sets in this set Builder Form A 149 so set builder form basically what is it common property what is the property Look sir all these numbers are equal 4 9 16 25 36 I understood clearly that a is to Squares of First Seven Natural Numbers If you understand then what will happen square off

21:58 first set of squares of First First Seven Natural Numbers this will be your set builder form Because with its help you can build this set. because the first seven natural numbers the square of is written see squares of first seven natural numbers or also write it like this can you a = x a = a i x where x is n where n is a Natural number from where n is a natural number You can also write the number like this You give the range of n like this also this This is a mathematical way of writing it this is done the english way this is done Both are mathematically correct, you also write this

22:44 you can also do this its set builder form it will happen ok this is also its set builder The form will be done, see what is the next one 1 9 25 49 so clear this is 3 square 5 square 7 square 9 square 11 square This means that you have to write it in English again. so squares of first six odd natural numbers one after the other because this time what it is odd it is simply odd numbers if it is square then what will happen to it Squires of first Six Odd Natural numbers like this are ok it is very easy

23:29 It is easy to find the first six odd natural numbers square 1 3 5 7 9 11 six done look sir How can I write it in maths language like this? How can we write x = 2n - 1 as an odd number? Write the value of a wire in the form 2n - 1 or 2n + 1 n is a natural number since n is a If I start with natural forest then forest will come And to get 11, I multiply n by 6, so n is a natural number from n is a natural number from 1 to 6 The mathematical way to write this has become easy This is an easy way, what's next sir, this is a big one It looks strange, what can you see in it I am seeing something, I am seeing something nice it's been great Think about it and see what you see

24:17 Brother, please see quickly what you are seeing I can subtract one from these directly I can't see it now but if I were one of these If I subtract it and remove forest from it, then forest will appear 8 will come out of this 27 will come out of this 64 64 in this 125 that is what is written here 1 p1 cube 9 write it down 1 p2 cube this Write it down 1 p 3 cube 1 p 4 cube and this Write down 1 p 5 is in cube form now you understand son 1 p n cube this is x 1 p n is of cube form where n is a Natural numbers from 1 to 5 This will be its set builder form fine Brother, I have separated the forest just a little bit Gave a twist to the story by separating the forest

25:03 All of them are being made into cubes all rights 2 9 28 65 126 you see 1+ n If the number is of type A then set builder Form is the statement through which you set Builder can build roster form The element in between after the curly brackets Write it down, it is called roster form Let's move on and not get bored any more I will do this, you will definitely set it off Natural numbers which are of greater and lesser magnitude 50 is written in set builder form see now I gave him the English maths part This made it easier to write set builder forms with math saying that brother the set of natural numbers Multiple of six to multiple of six We have to write and natural numbers and numbers greater than 50 If you want to write less then write the table of six

25:52 Brother just wrote the table of six and 50 Whatever is coming till now, I will give these numbers to you I want this which form of mine is this So son I have written the roster form but right now It is saying that you should write its set builder maths in the language x belongs to a natural number and x is a multiple of si gone wrong because in this the son goes till infinity If we go, we have to stay till 48, he said this I did not stop, I saw that multiple was written and the natural number is written somewhere to stop Brother, he is not saying much Infinite x is a multiple of si and x less E 50 this is also wrong why is it wrong because Son, here negative will also come because x Lesson: If 50 is multiple of 6 then it is also zero Everyone's multiple is zero, so everyone's multiple

26:38 is also a multiple of -6 so it has negative will also come so this is also wrong because We need a natural number, x is a It is greater than the multiple of six and zero See this is correct it is also written as natural So next option D was absolutely correct D Option son is absolutely correct Right Ok, I hope it is clear how I did it How I Created a Set Builder Form Roster form has been made easy, very easy Please see the question, any doubts, any problems Any Come on brother, we will move forward, we will move forward MT set now mt set you know what happens It is also called null set. We can call it such a set inside which there is nothing okay so something if it is not there then sir how is it set, is it set

27:23 son it is all set if i tell you that brother If someone tells you that there are such natural numbers tell me if it is negative then you can give some answer will you give me any answer, will you not give me this You will say it is zero, the answer is no, it is not zero The answer is that it is not possible i.e. that set If there is nothing inside then null set means A set that is not even possible, inside which He doesn't have anything present now like us Numbers have no value in maths We call it zero, just zero in the set I can't speak because I am zero in myself can be a set okay if i'm curly Let me write it in brackets, this is a set in itself okay so if i tell you something like this that which is not possible, that which is not possible or if there is nothing inside then you For that we use fi null set and Curly brackets are never used in fi phi represents the set in itself MT set or tap set means single ton

28:09 A single ton set is a set in which number of elements is one number of elements equal to 1 such as suppose any Tell me such natural numbers which are equal to two If it is smaller than then only one natural number will come one then any set has only one element Is Okay, this is the example, so this is your Single ton set will be many times JE's question The solution is a single one, it has already appeared in the papers Ton Single Ton means it has only one solution So sometimes a set is formed in which There is only one element, you can call it single ton can ok yes single single word Do you know what it means? Yes Sir, single turn means Single means one so a set in which there is one he element

28:54 It will be ok brother, I understood it, it is an easy thing Nothing! Hey let's move on Let's move forward Beta find it and infinite types of sets Understanding the definition from the name Find It Set It is possible to understand such sets in which finna Number of elements are infinity so in which infinity gay vo infighting If there is an element then this finaly it is set okay yes brother so as an example whoever has number of elements will be final it will be the final set in which the number of elements in fine it they infighting

29:50 Gaya means it has only two elements, so What kind of a set is this? Finaly it is a set, son. also fine it's set fine it's set g b the set of points on a line k Up above you know son infinity know hi infighting Let me ask you for an example, tell me this final it is set or infighting Quick Tell me quickly son, what did I say yes Let it stay on my head, you will miss it

30:36 If it is yours then think about it on your head, don't do this now Tell me sir I am bald Sir yes set of hair on your head your head what is the set of hair on you A lot of people would have I know what I'm doing wrong, now look at it why did you give an example because who are you you are making a mistake why are you making a mistake People are saying this because they are thinking this I cannot count how can I count I did not say that I cannot count They infinity to finna it is infa hair tere It is on your head, think about it, if it is on your head, son

31:26 Infinity, all over the world your hair is the only hair if it happens then it is not like that on your head, on your head, finish it There is a number of balls, you cannot count them if I could, I wouldn't have said that at all the definition of finda it set is that it You won't be able to count if five is all then finish it whether you can count or not can you count okay so set off your hair on your head is on your head is a final it set you are getting confused that you are counting I am not able to find it, I hope you have understood this He is saying, Sir, I am bald so I am a tap it's all set yes if you are gone then yours The tap is set That's fine brother, I hope this is all clear. Went yes sir it is a relative term that's why

32:13 I said that there is a child on your head I am talking about a general thing, every one of us I am not saying that everyone is obviously different We may be different but I am one I am talking about a particular student how many hairs on his head okay we are talking about a single child Here obviously you will not change the student If you can do it then it will not be well defined Let's write down equivalent and equal sets An equivalent set is one whose number of The elements are equal But equal set means the numbers are equal The given set should be exactly the same as

33:01 Suppose we are given a set 1 2 3 4 5 and Write this in any order you want 2 3 If 5 4 1 is written like this then how are these two sets It's an equal set, son; it's just a number of elements are same but with each one Its element is also the same sir please repeat it and write it If I give it yes, even then it will remain equal, accept it, break it Someone is forcefully repeating and writing it down Even then all of them will remain equal Because repeating it doesn't make any difference It is not ours come on son let's go ahead right equal and

33:47 The meaning of equivalent set is very obvious It has an easy meaning which you have understood now Only after this there is a superset and subset You understand the meaning of subset if a set yes yes I could have taken the example of 1 2 3 4 5 If I am there then there is some set which is a part of this For example, let's say I wrote 1, 2, 3, write anything. Just stay inside this, don't come out of it if you go then 1 2 3 what will happen b whatever will happen It will be called a subset of A and its symbol is b is a subset of a this is how c looks like but c is not the case think about union in such a way that There is a sign, it has been made crooked I have written it like this so this is called b is a subset of a if b is the whole of a The whole set is contained within a then b called subset of a okay and that would be a which The bigger set will become a super set okay so super so b is subset here b is

34:35 subset and a is called superset okay brother so superset and subset i think you understood the meaning of super I mean you know big and you know the meaning of everything if it is small then some part of it is a subset Now many times there will be confusion about what If I write the same set then that too Write down your subset which is exactly the same set If I write it down then it tells its own subset So if I take, say, an example x gave it and wrote 1 2 3 4 5 so same set is also a subset of itself x is a subset of a It is also correct to say that this sign was put in it We give you equality as you understand it What does equal mean, same set is also allowed Is

35:21 we are ok Brother I hope it is clear what color it is Brother Yes, I will give you another example Like the superset and subset you have I saw on the first page in the beginning that Brother, this is natural number and whole number, so Now tell me which of these is a subset that it is small basically see what is a natural number I can say that it is a subset of whole numbers yes because all natural numbers are included in it so natural number is called a subset of whole numbers okay then whole The number can be said to be a natural number It's a superset, okay, and look at some other Example: Someone else For example, z is a subset of natural numbers,

36:08 It would be correct to say z is a subset of z is a Why is the subset of natural numbers wrong? because z don't say whatever subset you are saying He is completely absorbed in her, just look at this Take z as a whole natural number It is not contained sir, there is negative also in z so Therefore it would be wrong to call z as the most natural word. It is correct to say the opposite, that natural number is a subset of z this is your correct It will go fine Yes yes i hope this is clear yes all these all of it will get complicated because complexion for all this set is ok bhaiya

36:56 I think you have understood that you are going too much into this I don't need too much basic stuff in it The funda is clear to you, let's move ahead Mounting Let's move ahead, see what is written here it has happened first it is written a set is a natural number and x len 8 so a which is the set he is gone 1 2 3 4 5 6 7 will be done son and bee So you have already been given the roster form I am 1 2 3 4 5 so clear B which is the best a is done b is a subset of a b is a Subset of AD options is clear and this symbol Do you understand the meaning of B is not a subset? of a I put a crooked line in it like this so Just like equal to and not equal to are something similar happened here not a subset of a

37:41 what does this mean belong to b belongs to a It is used for elements such as element like one is an element of b bol because one is a part of it one is An element of A, this can also be said to be correct if (a) = 1 then the sign belongs to the element It is used, I will tell you in detail later that element son belongs to sign just use the set for subset then be It should be okay, then it also belongs here It is wrong to say two A, then that element would have been there Speaking B is a subset of A, speaking correctly option d is correct easy next let's talk about this A little difference between the two Many children get confused that Sir When to apply this and when to apply that, so today we will clear this once and for all I have told you in very simple language

38:27 I told you whose subset's sign is this? Sign is a subset Whose sign does this belong to? To or in set theory we use it generally let's do this let's use this is an element is an element ok so if the value Take the previous example, take one set I take tooth 4 if I say I don't belong to you oh that's absolutely correct that's absolutely correct okay because one belongs to two or is an element of a it's absolutely right to belong it is also correct to say two a because two is also an element of a thee belongs to a ye It is also correct to say that four belong to a person is also correct if subset is to be applied then in this

39:12 put curly brackets because the subset is first it has to be set okay one no set if you put curly brackets in this one then you They will say that this is a subset, I understood brother, I understood Brother, I understood, I hope everyone understood that Curly It is correct to say that bracket one is a subset of a If it is written but one, then that element will remain If I write the bracket 1 2 then that is a subset of a it will happen because the set one and two together It will be made a subset of this too but one to one If I give it to you, it will belong to you, now you understand I think you have understood everything except Fi things are placed in curly brackets only then the set It gets set properly by itself There is no need to put curly brackets in Hei Fi. not needed If it had happened then I think you would have understood this basic funda what is the difference between the sign of belongs to and

40:00 Let's take another question inside the sign of the subset Let us take it from NCERT itself. has been raised but very very baby son this We do wrong, so once it's true, it's false quickly resolves the question of Look right, the first statement is saying Emma Put gusset bracket in B meaning made set It has happened, isn't it, the symbol is not a subset I have applied BC which is wrong brother it is a subset a b is contained within this a b which It is a set, whatever the order may be, it is a set of so this is false what happened False because not a subset of symbol is placed next a e is a subset whose symbol is this subset of x is a volume in what are the english alphabets ae i

40:46 oh you so what is this a subset of this ae yes It is absolutely yes sir it is absolutely yes so this one The second one has become true son because a Earning is definitely a subset, it is a subset, see next 1 2 3 is a subset of 135 where sir to is on Extra is coming on this, but there is none there is no two on this the whole thing The set should be contained within it, the whole The set is not there so this also becomes false curly bracket a is a subset of a b s True because the bud bracket has been installed That means once we have made a set then we can use the symbols will do that, will do this one and now element It is written curly bracket a naa this is false Why did he go because they made a set here given that if I remove this bucket from here and a belongs to a b c then it would be correct right curly

41:32 making a bracket meant they set it So the subset must be true okay i hope this is clear People mess it up a lot I mess you up, simple The set which is made in the language is in it This symbol and the element in it will look like this It will seem so, just understand this much, Understand the point Take Correct Is let's go ahead let's go ahead Let us take another example of NCERT yes this is a bit more complicated Let's take this one as well and finish it off in the bar so that there is no confusion left now

42:17 what did they do a little more in this It is cleverly shown that for the set A given First of all there are two lovely elements inside Given one two and a set, its element is I gave it to you, do you understand what it means, Curly To give a curly bracket inside a bracket means that this set is its element is the element of this set let me explain it I will explain it to you with a practical example what does it mean just assume your school goes on a picnic ok yes so assume you are in 12th A ok Yes, now whoever is the teacher or the principal They say in your school that friend We make sets for which children will go One person is saying that brother this is Mr. A will go Mr. X who is the headmaster of the school

43:03 He is a topper, okay, the topper of every class will go Let's understand it like this, okay so that x something also accept that a1 a2 a3 there are some children who There are toppers in every class, they will definitely go and The whole class will go to 12th class Everything will be completed because it is their farewell Bhaiya let him go, if everyone understands then this one what will become the set is a set inside which All these topper kids have some elements One is an individual and the other is the whole set means the whole class 12th this is also like this There are just a few examples, one of which is from your set has some elements and is also within a set An element is a complete set I hope you understand this I understood, yes I understood, I think I hope I understood this Did you understand what it means to give a set within a set what is it that you can relate to that you you are selecting the whole class

43:49 take it like this yes let's move on let's move on So son, now let's see the question what is he saying in this curly bracket 3 4 is a subset of A now this becomes false because this is its element is an element in itself then this element okay not a subset if it is a subset then you need to put one more curly bracket in it you will have to see in the element what were the 12 There was a subset sorry element so it had curly If you put bracket then what is this set Its element became false and belongs to meaning element this became true Understand Together with the F-Cali brackets, it is one element is the whole element of the set i.e. Allen's There will be a sign that belongs to you, this will be the sign

44:36 is true it is false if you get a subset I have to make you have more fun is to form a subset then this element has a Put a curly bracket and then it will be true because a curly bracket is then the element This is going to be one and you have applied this subset now become It's ok brother I hope this is clear one is an element of a one element is There is absolutely one element, true one is A subset having curly brackets in the wrong one wanted 1 2 5 1 2 5 is a subset exactly true exactly true 1 2 sorry 12 2 5 in curly brackets is set Yes True Exactly subset it means curly brackets have been put in 1 2 5 I made a subset and I am calling the element then false 1 2 3 is a subset of a now look at this this is really funny 1 2 3 now

45:22 Looks like it is 1 2 3 so the correct subset has been formed I did not become a son because Three is not alone You have nothing to do with Aayega Three you have to pick up the complete set of three or four You should have taken the element, this one is false It's done son, it's done Earth I gotta understand why because it gives you I don't want to see what's going on inside it You have to get the whole set, I have bought it there It was written 12th A, now go to 12th A, son It doesn't matter who is going you will get up the whole class and only then will you will go, did you understand, yes that's why more brain I didn't feel it was wrong to take the tooth, we did it this way I can't take it, if you wanted to take it then you should have taken it like this 23 4 and put curly brackets in it and this It is correct to say subset of A because it is called You will have to pick up the whole set

46:07 Fi is an element, then Fi is sometimes an element not only this is a subset this has become true false this is true curly brackets put fa I don't use curly brackets brother This is false, in Fa it is Fa It is a subset in itself, look at it brother Once a little quickly, someone in the part If you have any doubt then write that part in the chat Tell me, I will explain it again Tooth 4 You can tell by writing the numbering If you have any doubt then write it clearly okay c means clear and if someone If you want to write a question then write it in Roman Of give all correct sir sir please repeat eth eth

46:53 I will repeat it, look at this and understand this if you have it then you don't have 1 2 3 three nothing you have nothing to do with three Which child do you think is in 12th A? What does the whole of 12th A have to do with this? If the element was there then the same thing is happening here if you want to take it from three You have nothing to do with it so you They did not even go inside the set element If you want the element then take it completely and took 1 2 3 fur element and now If we had called this subset A then it would have been correct to have only three if it is wrong to take it then sir should I take it like this 1 2 3 4 Is this not a subset? Is this not also true? You would have a bud bracket in both of these It is necessary to apply it, only then it works fine brother sir Ninth tell me fi is an element brother fi So every phi is a subset Write it down of everything, I don't know this much If I haven't told you, tell me now

47:38 I give you Fi Fi is a subset of Fa is a subset of every set pick up any set in the world A subset of it will surely be phi because fa what is nothing if not nothing then everything Part of any set is nothing don't take any of it it will turn into a fu ok There is a possibility if I don't take anything you took it that time It will happen, it is clear sir so there is difference between 9th and 10th Sometimes curly brackets are used in a subset FA it is not so this one became true and this one returned false because there is no f element This statement will create the subset Ninth wala and 10th wala yours false and true Done Respectfully it's ok

48:24 Brother please tell me third sir look in third 3 4 element was with bracket 3 You understood it in 4 seconds, now it is an element You also need to create a subset of any element How to make a subset of a curly bracket I put a curly bracket on my side If you apply it from your side then it becomes a subset I hope this thing is cleared up in a second In the Third Tell me the difference number 11 sir anytime curly brackets will not be placed subset first It happens just remember this, look at me I never wore Curly Bucket or not All sets are not formed like this in all other sets A bud bracket is applied to form a subset then except but and f everything is bud to you Bracketing F is a subset of itself it happens ok

49:14 yes sir tell me fifth oh brother how is fifth The thing is forest is an element, isn't it, bud in forest If I put brackets then I would have formed a subset When we put a kali bracket in na na then we get a subset Ambulatory Well done son, let's move ahead and do the basic things. Now it is happening slowly, why is there power now But first we will count the number of subsets Brother let's arrange for the subset now What did I say, what is a subset? If I give you a set of A's Two is a subset of any number of you take the elements okay so its a What could be the subset? Just one taken What could be the subset just to take one subset can be you take both one and two I made the whole set myself and got a

50:00 always happens then how many subsets does it have There are four subsets of the set A which are Subsets He became four, one took only one only one only two elements both one and two or nothing or nothing at all you have to take Right, let's do it, this matter is over If the subsets are taken out in this way then the number Looking at the off subsets a formula can now be created let's say inside this there is 1 2 3 4 Suppose there are elements in the subset What would have happened, sir you did not say anything and you took one element one then Took only two then took only three then I took only four and now I think I took two each So now it can have NCR if it is common

50:45 So what is the number of subsets that will be formed? number of subsets will be formed that sir firstly If you did not take even one then 4c 0 not even one So only one set will be formed nc0 or any other means plus one element taken means in four If you select one of these then it is inside the subset How many elements are there, there is one element then Maybe you have bought dodo ones like this One two will become 4 to 2 as many times as I can select two elements from P4 S3 will happen when you have three elements subsets would have been created and 4 c4 is just a 4 c4 then there is only one this set in which If you have taken all four then this is yours Let the number of subsets be and its formula I have already told you brother that the power of 2 is n You guys have read 2 in Bano Miyal

51:32 power 4 is right so in general if n Suppose there is a set having elements A there are distinct elements son please note There are distinct elements n then The number of subsets will be 2 to the power of n nc0 p nc1 p nc2 up to n a bano miyal The formula for this is the total number of sets if a set A contains a distinct element number of The formula for the set will be t to the power of a Extremely Important Formula of Today Understand the most important thing about class The formula is now Tak sir what is NCR oh wow wow wow Brother what are you talking about NCR That is our Bano Miyal Kafit you don't know what is NCR So now you understand the derivation of 2 to the power a

52:18 what is it you took first because derivation Also important are the zero elements out of n then you took one element again you took one element again Three elements inside a two element subset and in the end you took n from n in the subset and its formula is 2^n So the derivative here is 2^ n now let's do one more thing in this one more If something happens, I will tell you the proper thing The next proper subset name is written as subset is like suppose I told you Given an example, there is a set 1 2 then one of them I took a fa in it, took a one and took a two and I bought that bean set So the same set which we have taken, if we minus it If you do that, then we call those remaining subsets are proper subsets then if I consider its proper

53:04 Let me talk about subsets, proper subsets then these become proper subsets basically If you subtract one from that whole set, that means That one particular case in the proper subset When you minus all n elements So many proper numbers are being selected The subset will become zero, one, two, and Lastly, the one taking bus from nc1-1 to n You don't have to take all the elements in one case When you have selected, you do not have to take this case So obviously the value of this thing is 2 to the power n one of those particular cases is minus will go right to the power of 2 n -1 number directly of proper subsets then for any In the set For example, there are five elements A, B,

53:49 If you ask for CD number of proper subsets then total set 2 to power 5 2 to power a Filled the form -1 finished, understood it so simple The value of n is five because five elements and 2 to the power n - 1 is this one I used the formula to get the number of Proper subset so 32 - 1 31 the answer is C Easy question will become easy right Question: Number of proper subsets written in total subset 2 to the power of n simple okay Suppose there are 10 elements in a element then the total Number of subsets of 2 to power 10 any 50 The total number of elements in the subset is a power of 2 50 proper questions -1 to be answered is as simple as that ok now this is a little bit basic

54:37 A little bit about the basics, now let's discuss about JE Questions will come son, till now just look at the theory Tell me I've only done a few more things in the last hour only conceptual kids who know very basic I was starting with teaching them all the basic fundamentals I have cleared them, now let's see the number of subsets Let us look at one or two questions given in a set one two three up two ok its the power of total number of subsets It will be 100, it is that easy, will anyone ask No. of Non MT Subset Good Non MT Subset of a truth that is product of elements In A is even understand what is your question is to form a subset such that the product of If the element is even, it means you don't take it I could 5 because when I put cream in it then

55:25 If the product of the element is not even cannot take this cannot take such a subset what else can I take then can I take this sir 1 3 2 1 2 3 because when you multiply If I am here then it means you understood my friend At least you should take one even, not all odd I understood that you can take it, so clearly I understood it that if I want to insure that If the product of the element is even, then it means a At least an even should come because As soon as an even number comes, multiply it By doing this he will make it even so total Subsets I subtract that from the total subset when no even number is I understood that if I select all the subsets The power of which was 100 what was the total 2

56:11 that the power was 100 and he would have subtracted it from it I mean whenever you select an odd number Select odd number, odd number means no Even numbers mean you can subset all the odd numbers What are the odds being made sir? It is 50 odd So understand it like this, we have to make subsets of this, 1 3 5 7 such that subset of odd numbers are 99 will it be made or power of 2 will be made 50 if you understand I want at least one even so I took total I subtracted the amount when someone came no when will no one come when all the odds are in Out of all the odds, how many will be made 2 50 to the power of 2 becomes 50 to the power of 2 Son Look right, take the power of 2 to 50 common

56:58 take 2 to power 50 common 2 to power 50 My answer has come as an option It is visible right here too So beta permutation in permutation set In many places, understand the meaning of permutation in reverse way I seem to be set in some questions I will ask you a lot of questions today having such permutations PNC guys let's go, I hope this is clear what i did is remove all the subsets I added minus when the even number did not come if he stays then he will be assured that at least one An even number will come because I have to get at least If I get an even number then I am a subset The product which is a product of the elements even come

57:43 It will be okay brother repeat sir see one more time Le Sir But Even if we talked about it then son total subtract the odd from even then there is no even left Do you understand what I want, I want hmm at least one even should come now turn it upside down think if you want at least one even to come If it goes then subtract it from the total when it is even If I subtract that from the total it did not come When even numbers do not come If even numbers do not come Who came odd because apart from even and odd If there is nothing then even did not come which means all are odd How will the odds come, sir how many are these There are 50, so when their subsets are being formed among themselves The number of subsets that can be formed in 2 to the power of 50 I will minus those which will form subsets. From all the given ones, subtract those which are in the subset If I was getting only odds, would I be saved?

58:28 In which at least one even must come At least one will definitely come It will go fine Brother I hope this is clear yes sir why not d u's power is one out of 100 why don't I minus 2 to the power of 100 What basically do you do if you subtract one from he is calculating the total, only odds are there in it People will also come, then we don't need it

59:14 You just told us the total I shouldn't have come this way 1 5 this is so The problem is that this one is not coming for us should let's move forward let's come to the next one son let's go next Let's see another JE's question are the subsets over a is this 1 2 3 4 5 6 7 ok brother listen carefully a set diya is a to b given 3 6 79 number off Elements in the Set Now look at the language of sets it is confusing that c is a subset of a this what is written c is a subset of a ok It is not proper, both are not equal The written equal is also given i.e. same The set is also allowed, C and A can be equal

1:00:00 if c is the intersection b is not f of c and b There should not be any intersection, if you understand What are the numbers of elements telling you? In this set C language is very confusing whoever understands the language sees it in the set His question will be correct in Lee set because it doesn't take much brain Once the language is decoded there is a set of b is a set number of elements of set mean How many such cases do you need to tell in new set C is an element that is a subset of A, and C does not have intersection with B should f should not be there then it means when Subtract the total when the intersection is is so total subsets of a total subsets of

1:00:46 I am finding the value of A AC, number of Elements in set C will be total subsets of a minus n minus number of Subsets Number of Subsets not an intersection c is f an intersection sorry what is written s intersection b is F means basically that set is a subset of it and There should not be any intersection of these two So we can conclude that F is Pa and that is I will minus that from the total I will minus when the intersection is coming I hope you understood this

1:01:31 yes we will listen carefully so the total number of How many subsets of a are there to the power of 2 given 7 what happened so much 2 became 7 power why because the formula for 2 to the power of n I have put it there are seven elements 3 4 5 6 so What we did was we calculated the total by the power of 2. removed the subsets now that minus from this will do it when the intersection is happening What is the meaning of intersection, what is the meaning of phi no intersection is coming intersection what's coming look what's coming intersection there is a th at the intersection sir one is coming okay what else is coming ch is coming sir Common intersection means common in both I know this much basic, let me give you We will read about the intersection later, but we know this much so these two elements are your intersection

1:02:18 you want to take out that If the intersection is complete, it means use both of them Be careful while creating subsets Listen, I don't want to use both of these. whatever you want to write in minus because I I wonder when their intersection will come When nothing will come common nothing will come When will common not come when its common uses If you don't want to do it then make a subset like this When these three and seven are not being used at all and six sorry because some of the three and six If it is used up then the fee will not come again If Fa does not come right then it means three and six Ignore it and think that it doesn't exist make subsets of the remaining ones Make a subset, one doti cha pa means five subset of elements means power f of u

1:03:04 I understood it Now look oh sorry sen is also there yes sen is also there I saw it wrong sorry sen is also We will have to fly Sen too, part of it I understood because three, six and seven brothers come together Look at the intersection, I made a mistake it's done, three are coming here These three will have to be ignored and 6 more 7 + 1 + 2 + 4 + 5 means now there are only four elements i.e. beta 2 to the power of 4 It will happen sorry I did not see Sen too The intersection is being part of the Apart from six, sen is also coming common. Ignore those three so that nothing happens they should not become common because if these three If you have created subsets by ignoring the intersection 100% F I understood it, I understood it, then it means the answer is

1:03:51 2 to the power of 7 which is 128 Subtract 16 from it give me 112 answers are coming brother 112 answers are coming yes 112 I got the answer, look at the language How tough the language was, I would have explained it again once again brother i have given you a couple of sets Number of elements to be given in set C which is a subset of A is a subset of A from here I figured out that I needed to raise n to the power of 2 I have to count the number of subsets but Given a condition that their intersection be should not be its intersection with b There should not be fa because not equal to I have written F, it should not be F I have written total I subtracted 1 from the intersection point when

1:04:36 Having intersection doesn't mean having anything in common Nothing should come common, when will it not come When you did not even take the common people there are 3 6 sa so the common ones are 3 6 sa Make a subset of the set without them. Ignore them. Kill it because if it comes then there will be an intersection f will not be formed if it is a subset of these If it continues to be built then the intersection will be will go sir there is nine in b also let it be in b what do you have to do with nine b then a The subset f does not have intersection with b okay so what is it in a What is important is what is in B and what is in it You have to pay attention to the intersection We have to find out what is the intersection between the two The intersection is three, six and seven, I hope so It is clear that you have to ask such questions Son, you have to use your brain a little bit in JE

1:05:22 There is a little bit of butt in it at the end of the class By then you will understand how you used this brain This goes, I am getting a question asked as well Nice integer type It can also be made like this in

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