Class 11 Maths Sets Intersection of Sets

Intersection of Sets

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.

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}.

Numerical: Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∩ B.

Solution We have A ∩B = {6, 8}

In the Venn diagram below, area in the green represents A ∩ B

 

Disjoin sets

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 called disjoint sets, because there are no elements which are common to A and B

 The disjoint sets can be represented by means of Venn diagram below. There is no common area shared by A & B, thus A & B are disjoin sets.

 Some Properties of Operation of Intersection

 (i) A ∩ B = B ∩ A (Commutative law).

 (ii) ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ) (Associative law).

 (iii) φ ∩ A = φ, U ∩ A = A (Law of φ and U).

 (iv) A ∩ A = A (Idempotent law)

 (v) A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) (Distributive law ) i. e., ∩ distributes over ∪

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