Set Theory in Grade IX

Hello friends, in today's session we are going to learn about Set Theory. Set theory is a branch of mathematics that study sets which is a collection of objects. As the set can be a collection of any type of objects but the Set theory is a collection of objects that are relevant with mathematics.
The theory begins with a fundamental relation between the object O and a set S. If our object o belongs to our set S then it is represented as O ∈ S. where the symbol ∈ says “ belongs to”.
When we take two sets into consideration then we have different results known as set inclusion.
Like if all the members of set B belongs to set A, then it is called B is a subset of A and the set representation is done as A ⊆ B.
The members of set B could be 1, 2, 3 and then the members of set A would be 1, 2, 3, 4 ,8.
So we can see that all the members of set B are in set A.
Like this we have some simple relations that we need to know.

1. Union – when we do the union then we do is simply write the members of both the sets together. For Example the members of Set A are 1, 2, 3 and the members of set B are 1, 2, 3, 4. Then the Union of these sets will have 1, 2, 3, 4 as its members. And it is represented as A ∪ B.
   
2. Intersection – for intersection we just take the common term from the given sets. For Example- set A has 1, 2, 3 and set B has 1, 2, 3, 4. so the intersection of these two will be 1, 2, 3 and it is represented as A ∩ B.
   
3. Set Difference – Like if we have two sets, A and B, denoted as A / B. if Set A = 1, 2, 3 and set B = 2, 3, 4. so A/B = 1, 2, 3/ 2, 3, 4 = 1 and B/A = 2, 3, 4/ 1, 2, 3 = 4.
   
4. Symmetric difference – if we have two sets A and B then their symmetric difference is given by (A ∪ B) (A ∩ B).
   
5. Cartesian product – it is generally denoted as A × B. is the set whose members are all possible ordered pairs. It is written as (a, b) where a is the member of set A and b is the member of set B.
   
6. Power set – If we have A as our set whose members are all possible subsets of A. Like A = 1, 2 then its power would be , 1, 2, 1, 2 .
   

Some basic sets which do come are the empty sets, set of natural numbers and the set of whole numbers.
So now you seems to have got all the basic knowledge what set is and you would be able to solve questions based on it.