00:00So now what we are going to discuss is set, so what is the literal definition of set and set
00:05is a well-defined collection of distinct objects which we call elements as well as members of a set
00:13Is
00:13So then there is a set of bicycles in the bar, you can do a type of gym, there is a box like
00:19That this is a box, the items placed inside it are its elements
00:25We can say that elements are the elements or members of that set, then in the bar, like this set,
00:33If so many elements of Indra are 1,2,3,4,5,6 in this type
00:39This is the element or the set or its members, so now we have mainly two ways to present the set.
00:46There are ways, the first way is
00:49This method is also called rot or tabular form, so what do we basically call it like
00:57that someone set this
00:59We will write element, what are the elements of a set, elements of a set, for example, this is like a crazy person.
01:09that there is a set in our leaves
01:11So then in the matter of set, first of all we will create this bracket on both sides of the element, then
01:18If you write element in the text then in the text
01:21Jot this in tabula form with any number of elements, let's write them all 1,2,3,4,5
01:286 goes on writing like this
01:31But suppose there are 1000 elements of this form in many sets, then it is difficult to write
01:38If I could, what would I do with it? Add it in tabular form.
01:46We put its jot in the jot bar and write the final element as 1000 or if the final element
01:55Apart from the fact that the final element is 103, I can also
01:58This is 1,2,3,4,5 dot dot dot, if we want we can write something at the end also.
02:051001,1002,1003 can also be written in this way. There are many types of sets for one value.
02:14Let's assume that the number of elements in the set in our par becomes infinite.
02:20Like there is infinite number of elements, so what we will do is 1,2,3,4,5 as per our requirement
02:29Write down some starting elements next.
02:37If you tie it with this method then more...
02:41Or next time you present the form in the form but you must have done that before
02:53It is not necessary that the element sequence contains 1,2,3,4,5 in this sequence.
03:00Value lizzy element in our par what is this set of
03:04It is a well-defined collection, which means we will follow some pattern or else we will not follow this pattern.
03:13We will be able to do it with dots, if we do not follow any pattern then we will do it basically like 1,3,6,7,8
03:21If it is of this type then I will write the element
03:25that it will write down all the elements that the elements inside it are not following any pattern, if there is any reason
03:32Some of them are written down, which means they will follow a pattern, it is not necessary that the pattern will remain the same.
03:38This is like Api's
03:49The pattern of the set can also be like this. The pattern of such a set can also be like this.
03:55Equal to the first element to four sixes at this also became an example of AP
04:02That's why this pattern can also happen that you are four at sixty-two, now you will continue to go ahead
04:13If we consider one and twenty eight, then it is not necessary that the element of the set is of the same type.
04:21Follow the pattern Anyone can follow the pattern
04:27And if I do not give all the elements in the registry then try this type that we will give the next element
04:35I can do it myself
04:37And if the elements of that set do not follow any pattern then I will remove all the elements in the question.
04:43will list it by this type
04:45And in the zone site this bracket will become curly bracket now this is done in written or tabular form
04:54Now next comes the set builder form which is also most generally used in the question set builder
05:01form
05:03What does this give us inside of J, let's say J is a set in our set
05:09a is equal to
05:12If any element of this set A is x, then in what type will x appear before x in the statement
05:21We will put this dot dot first of all
05:23Then in the statement we will write x comes in this x comes in set so that this example statement
05:35I will first remove the arg as if writing any set a in set builder form
05:39So what will be the element of a is equal to a, how many x and x come in my par
05:46will define x by their x is equal to
05:50This n plus 1, what is n, n comes in natural numbers and n, which is n is the most
06:04First we will write that value n is less than
06:10n is less than 2, n comes in natural numbers, so we wrote this in set builder form.
06:19set
06:19So what will be these elements, first of all we know what natural numbers are.
06:251,2,3,4,5 but what condition do we give that n will remain less than 2 i.e.
06:34natural number 1 with 2 to shota
06:36So if we make this a set, it will have this many elements.
06:401 plus 1.2 means one element x becomes 1 plus 1.2
06:47x to the remainder 2, 2 to the remainder i to n, that is, the remainder will be an element of a.
06:54can also give us o from x a is equal to a is equal to x
07:04And what is this x, x is equal to, this will define your x, how to find x
07:09n upon 2 is n divided by 2
07:32That is, 0.5 comma then 1,2,3,4,5,6,7 in the bar, this element is natural
07:44up to number 7
07:45But if you are short of 7 then we will not consider 7, now keep doing it.
07:50n of 1 by 2 0.5 2 by 2 1 1.5 2 and 2.5 and 3 so on
08:02These 6 elements 1, 2, 3, 4, 5 came across us.
08:06Now suppose I want to define a set directly from b
08:11If we want to define a from b then that b is equal to x and the x is
08:20x is less than 2
08:26x 2 to short comma this up we have defined this directly over x so I
08:33There is no root to write n etc. x comes in a, which means x is equal to a.
08:41element in
08:41So, if we define the set a of b then what are the elements of b?
08:46what will happen
08:47So first of all what is this x, x is the one inside a, that is, it is one of these elements
08:54x elements and that by 2
09:00Sota is satisfying and is also in a, that is, 0.5 will come in such a one.
09:06will go 1.5 it will not come 2 because
09:09This 2 has become equal to 2 but here the sign of let due is given, not
09:15Let then o equal to so this b which is set
09:18We have 0.5,1,1.5, so in this way we have divided set A into set B.
09:26which was also made
09:28Now we have so many elements 0.5,1,1.5 in our set, then what is the total number of elements in set B?
09:34You have become ours
09:36Now we have seen the set builder form and the rote or tepula form, now this is the representation of the set.
09:44Now the method has been
09:45There are basically many types of sets, so here we go: types of sets
09:58So basically there are many types of sets in our par but it does not have zero in it that one
10:03set of these
10:04It can be of the same type but it can also be of multiple types simultaneously, so first it is null
10:09Let's see the set
10:11Like what is null set, it is known from the name, meaning of 0 and null means this
10:17The number of elements inside the set
10:25For example, if a set is a null set, then it will represent something like this or FICOMA like this.
10:32You can see it represented by creating a symbol inside it.
10:35It means null, that is, there is not a single element inside the set, for example, we can basically call it
10:42You can argue that this is an empty box.
10:46Then later comes the singleton set. What the name singleton set suggests is that inside the set
10:53There is an element such that a is equal to 2. This singleton is set.
10:58Similarly, a is equal to 3, this is also an example of singleton set, b is equal to 5, i.e.
11:07that the set must contain a key element
11:11So then later that singleton set will be now next in our footer this equivalent set so equal set
11:19This is known from two sets
11:21For example, in equivalent set, what is the set a in my foot 1,2,3 similar distant set
11:32b b in our foot 7,8,9 so we can see inside these
11:39a also has three elements or members and b also has three elements.
11:44So what are these two, equivalent set, equivalent set means the members inside both of them are equal, know
11:52That this also has three members and this also has three members or elements, then what should these two be in the bar?
11:58equivalent set, then comes the next time, equal set, the number of elements in an equal set will also be the same, element
12:06will also be the same, for example, a is equal to 1, 2, 3,
12:12a is equal to 3, 1, 2, so both of these will be set equal, how is that, this is set,
12:22The order of these rate elements does not matter, like we can also write 1, 2, 3, 3, 1, 2
12:29How is that, we have put 1, 2 and 3 in a box, 3, 2, 1 in the door too.
12:36Now it is not important which one is placed on top and which one is placed below, but basically the box is the same, because
12:43If we apply that formula, then the elements can be above or below, that is, both within the equal set, number
12:50of elements will also be the same, and the element that is there, that too,
13:26The larger set will come towards this, meaning open face.
13:33Basically we can remember it by this symbol, it's less than or equal to, so then it's
13:38In, if in our leaf, A is a subset of B, that is, an inner number of
13:45elements, which this symbol is not literally, it is just a trick to remember, in the form
13:52I recall,
13:53a is less than or equal to b, meaning a is smaller than b, i.e., a is a subset
14:00and b is the superset, so the definition of both of these is, here a is the subset
14:07and b is a superset, which means that, let's say, inside b,
14:12From the element, 1,2,3,4, then in the bar, what could be the elements inside a,
14:21The elements inside a, it can only be in all four of these, it will either be all four, or
14:27Then it's going to be 3, any 3, so basically, what it means is, whatever is inside a
14:33From the element of, that same to go same b from being picked
14:37can be 1, 2, and cannot be more than 1, for example, the elements of a can be 1, 2
14:43, could be 3, from a, a it could be 1,2, could also be 1,2,3,4
14:52But a will never contain more elements than b, because a is a subset of b, meaning
14:58What we basically understand is that by taking some elements from b, we created a.
15:03is given, so a can also be a null set, so let's say we have an element
15:09If b is not raised, then a null set will also be the subject of b, later a super set
15:16What happens is, here a is a subset, and b is a subset, then a is a superset, that is, b is a superset.
15:25Yes, or you can also warm your lips with this, in this case also
15:30b is the superset, a is the subset, that is, b is a box inside a, we have defined the same
15:36Created a from element a, that is, whatever element is in a in b, is present in every element in b
15:42It must be present, there cannot be any element in a which is present in both a and b.
15:47If not, then this means that b is a superset of a, then later
15:53what does proper subset mean in, let's say a, what is the element in our footer, in a
15:59The elements in our foot are 1,2,3,4, so the elements in b will be these ones, this
16:07There will be 1,2,3,4, but there will be one element extra in b than a, that means both
16:17The number of elements inside a is not equal, b has one
16:20element extra is not necessary, a can have more than one element extra, but b of both
16:27Its elements will not be equal, so later, a is a proper subset of b, what can we write like this
16:35We can create this symbol, a is a subset of b, and what will be the type of subset, proper
16:44subset, because it satisfies the definition of subset
16:48Every element of a is present in b, i.e., a is created through b, but in b, a
16:54The element extra of is equal to one, that is a of b, basically, simply put, a is a subset
17:01of b, but both a and b should not be set equal, then later, proper value of a, b
17:06subset, then later, on the universal set, what does universe mean?
17:12in finite, that is, whatever phi can be imagined, it converges in the universe, so basically, the universal set
17:21In, all elements are in the universal set, that is, if we imagine any element, for example, 0.5,
17:291, 2.5, root 3, any element that we can look at, all of them are in the universal set.
17:36Hong
17:43It is subscribed. We have one set, one set for example one set, that me together, three
17:53The accompanying set may also contain.
17:56For example, this next step in our chapter is a finite set. What this means is that the number of elements will be finite.
18:03Like 1, 2, 3 became finite
18:06is equal to 1,2,3,4,5 up to 100 this also became finite but 100 is that
18:16But it is finite but it will continue in infinity.
18:20is equal to 1,2,3,4 up to infinity, so now in the question we said that a
18:29The set of key types can be of several of these types
18:31For example, in our leaf a1 is a null set which does not contain any element and in our leaf b
18:39The set is 1,2
18:42So here a null set is created and along with it a subset of b is also created and a
18:50a becomes a subset of b and a also becomes a proper subset of b
18:54So then it is not necessary that any set be of type A at a time.
18:59If one of the types is of type A, it can also be of multiple types at the same time, due to which
19:05Inside
19:05Then the next thing in our discussion is power set, so what is power set, basically our leaves
19:12is a set in a
19:13a g suppose b is a set then 1,2,3 in my leaf will form so many subsets
19:23All of them will be set to its power.
19:27That is, the power set of all possible subsets formed from b is
19:36will be called
19:38for example, if we write its power set of a, then it will become this power set of a is equal to
19:50x and x is subset of a
19:58Here it is not a but b which we can write as power set of b is equal to x
20:04and x is a subset of b
20:09So what will happen to the power set of b is equal to what will happen in our case
20:15The first thing that will come to our mind is the Pi tap, not the Pi, this is the tap tap.
20:22That means null, that is, there is no element, that is also possible 1,2,3
20:28individually then 1,2 si,2,3 and 1,2,3 and finally this 1,3 we put bool
20:46If you go then 1,3
20:47So how many elements are there in it 1,2,3,4,5,6,7,8 so there is a formula for it also
21:06If there are n elements in a set b, then the number of elements in the set
21:11How many elements will be there in the power set of 2 to the power of n? The elements of its power set will be equal to n, so this
21:20How can we create a power set?
21:22We can also take A instead of this power set simply by saying that A is equal to this pi.
21:27,1,2,3,1,2,3,1,3,1,2,3 so we can say it in this way also
21:43So the next topic in this matter is Venn diagram.
21:49In a Venn diagram, what we basically do is we divide the sheet into three parts.
21:56So do that in the next video
21:58What happened to Zhao's life
21:59You can also swing which is tied with a swing.
21:59I am going to beg for help, this is my shame
21:59Remains, remains, also remains
