**Intersection of Sets: **Given 2 sets A, B, then the set formed by taking the common elements of the set as its element is called intersection of set.

In general, intersection of n-sets is the set in which every element is present in all the n-sets A_{1} **∩** A_{2} ∩ A_{3} … **∩ **A_{n}

\(\bigcup\limits_{i=1}^{n}{{{A}_{i}}}\)** **= {x | x Belongs to each set of A_{1}, A_{2}, …, A_{n}}

A **∩** B ⊆ A, A **∩** B ⊆ B, A ∪ B

Two sets A, B are disjoint if A **∩** B = ø

N sets A_{1}, A_{2}, A_{3}, … A_{n} are pair wise disjoint if Ai **∩** Aj = ø, i ≠ j

**Note: **A **∩** B is denoted as AB. Similarly A **∩ **B **∩** C is denoted as ABC

**Properties of intersection of sets:-**

1) A **∩** A = A (Idempotent property under intersection)

2) A **∩** B = B **∩** A (Commutative law)

3) A **∩** B **∩ **C = A **∩** (B **∩** C) [Associative law]

4) A **∩** ø = ø

**Note:** If 3 sets A, B, C are pair wise disjoint sets then A **∩** B **∩** C is a null set .But the converse of the statement need not be true.

⇒ In general A_{1} **∩** A_{2} **∩** A_{3} … **∩** A_{n }= ø

(Converse need not be true)

⇒ Given two non – empty sets A, B and μ assume that A & B are not equal. Then draw Venn diagram in fig cases:

**(i)** B contains A (A ⊆ B)

A ∪ B = B

A **∩** B = A**(ii)** A contains (B ⊆ A)

A ∪ B = A

A **∩** B = B**(iii)** A, B are disjoint sets

A **∩** B = ø**(iv)** A intersection B non-empty setNote: If A ⊆ B, then A ∪ B = B

A **∩** B = A

Result: Union is distributive over intersection

Intersection is distributive over union.

A ∪ B = (B **∩** C) = (A ∪ B) ∩ (A ∪ C)

A **∩** B = (B ∪ C) = (A **∩** B) ∪ (A **∩** C)