Usually, the Set Intersection Operation takes only the elements that are in both sets. The intersection is nothing but the overlap of two sets. Solved Problems on Intersection of Sets helps you get an idea of how to find the intersection of two or more sets. To learn more about the Operations of Sets refer to the **Set Theory **and clarify all your concerns. Check out the Example Problems on Intersection of Sets explained step by step.

## Intersection of Sets

The intersection of Two Sets A and B is nothing but the set of all the elements that are common to both A and B. It is denoted as (A ∩ B) and is read as A Intersection B or Intersection of A and B.

The Intersection of Sets A and B is represented as A ∩ B = {x: x ∈ A and x ∈ B}

### Solved Examples on Intersection of Sets

1. If A = {1, 4, 3, 7, 9, 12} B = {1, 8, 3, 4, 7}. Find A ∩ B?

Solution:

A ∩ B = {1, 4, 3, 7, 9, 12} ∩ {1, 8, 3, 4, 7}

= {1, 3, 4, 7}

2. If set A = {2, 4, 6, 8, 9, 12}, set B = {1, 3, 5, 9, 15, 18} and set C = {2, 3, 5, 6, 7, 10}.

(i) Find Intersection of Sets A and B?

(ii) Find Intersection of Two Sets B and C?

(iii) Find Intersection of the Sets A and C?

Solution:

A ∩ B = {2, 4, 6, 8, 9, 12} ∩ {1, 3, 5, 9, 15, 18}

= {9}

B ∩ C = {1, 3, 5, 9, 15, 18} ∩ {2, 3, 5, 6, 7, 10}

={3, 5}

A ∩ C = {2, 4, 6, 8, 9, 12} ∩ {2, 3, 5, 6, 7, 10}

= {2, 6}

3. If A = {x, y, z} and B = {ф}. Find intersection of two given sets A and B?

Solution:

A ∩ B = {x, y, z} ∩ {ф}

= {}