Intersection of Set, Properties of Intersection - Practice Questions & MCQ

The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘∩ ‘is used to denote the intersection.

 Symbolically, we write A ∩ B = {x: x ∈ A and x ∈ B}

For example, let A = { 2, 4, 6, 8 } and B = { 2, 3, 5, 8 }, then A ∩ B = { 2, 8 }

If A and B are two sets such that A ∩ B = φ, then A and B are called disjoint sets.

For example, let A = { 2, 4, 6, 8 } and B = { 1, 3, 5, 7 }. Then A and B are disjoint sets because there are no elements which are common to A and B.

Properties of intersection

• A B = B A (Commutative law).

• ( A B ) C = A ( B C ) (Associative law).

•  A  = , 

• A  U = A (Law of and U).

• A A = A (Idempotent law)

• If A is subset of B, then A  B = A

Distributive laws

1.  A ( B C ) = ( A B ) ( A C )  i. e., distributes over

This can be seen easily from the following Venn diagrams

LHS:

RHS:

2. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) 

This can be seen easily from the following Venn diagrams

LHS:

RHS: