The **intersection of two sets** A and B is the set of all those elements which belong to both A and B. Symbolically, we write

A ∩ B = {x : x ∈ A and x ∈ B}

**venn diagram of intersection**

**Some Properties of Operation of Intersection**

- A ∩ B = B ∩ A (
**Commutative law**) - ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ) (
**Associative law**) - φ ∩ A = φ, U ∩ A = A (
**Law of φ and U**) - A ∩ A = A (
**Idempotent law**) - A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) (
**Distributive law**)

**Example of intersection**

**Example **Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7 }. Find A ∩ B and

hence show that A ∩ B = B

**Solution **We have A ∩ B = { 2, 3, 5, 7 } = B. We

note that B ⊂ A and that A ∩ B = B