CLASS-8
INTERSECTION OF TWO SETS

INTERSECTION OF TWO SETS

The intersection of the sets A & B is the set of all the elements which belong to both A & B, it is denoted by A ∩ B and that should be read as ‘A’ intersection ‘B’. we can write, A ∩ B = { x : x ∈ A  &  x ∈ B }

If A and B do not have any elements in common then A ∩ B set will count as a null set, A ∩ B = φ

There are some example which are given below for your better understanding –

Example.1) If A = { 2, 4, 6, 8 } and B = {  6, 8, 10, 12, 14 }, then find  A ∩ B = ?

Ans.) as per the given condition we can find, A = { 2, 4, 6, 8 }   and B = {  6, 8, 10, 12, 14 } and I have to get the answer of A ∩ B = ?

       A ∩ B  =  { 2, 4, 6, 8 } ∩ {  6, 8, 10, 12, 14 }

                =  { 6, 8 }

So, the desired answer is  A ∩ B  =  { 6, 8 }

Example.2)  If A = { a, b, c, d } and B = { d, e, f, g, h }, then find A ∩ B = ?

Ans.) as per the given condition we can find, A = { a, b, c, d }  and  B = { d, e, f, g, h }  and I have to get the answer of  A ∩ B = ?

           A ∩ B  =  { a, b, c, d }  ∩ { d, e, f, g, h } 

                    =  { d }

It has been seen that, there is only common element of both the sets is ‘d’ 

So, the required answer is A ∩ B =  { d }

Example.3)  If A = { a, b, c, d } and B = { w, x, y, z }, then find  A ∩ B = ?

Ans.) as per the given condition we can find, A = { a, b, c, d } and B = { w, x, y, z } and I have to get the answer of A ∩ B = ?

           A ∩ B  =  { a, b, c, d }  ∩ { w, x, y, z } 

                    =  φ

 It has been seen that, there is no common element from both sets A & B

 So, the required answer is  A ∩ B =  φ

Example.4)  If  A = { a, b, c, d, e }, then find  A ∩ A  = ?

Ans.) As per the given condition, we have found that A = { a, b, c, d, e }, we have to find out  A ∩ A = ?

   So,  A ∩ A  =  { a, b, c, d, e } ∩  { a, b, c, d, e }

                  =  { a, b, c, d, e }

                  =  A

 So,  A ∩ A  = A

If all the elements of both the sets are the same then the intersection of the same sets will be the same as given sets, it is called laws of operations on sets

Example.5)  If  A = { x, y, z } , then find   A ∩ φ = ?

Ans.) As per the given condition A = { x, y, z } ∩ φ = φ, because there are no elements of the Set A are similar to null set φ.

Exercise.6)  If  A = { 1, 2, 3 } and B = { -3, -2, -1, 0, 1, 2, 3 }, then find A ∩ B = ?

Ans.)  As per the given condition we can find, A = { 1, 2, 3 } and B = { -3, -2, -1, 0, 1, 2, 3 }

 Now,  A ∩ B =  { 1, 2, 3 } ∩ { -3, -2, -1, 0, 1, 2, 3 }

                = { 1, 2, 3 } =  A

      So,   A ∩ B =  A, where  A ⊆  B  

      So, when  A ⊆  B, then A ∩ B =  A    or

         If      B ⊆  A, then   A ∩ B =  B

 Above are called laws of operations on sets