# CLASS-11OPERATION ON SETS - INTERSECTION OF SETS

OPERATION ON SETS -

(2) Intersection of Sets

The intersection of two sets A & B is a set that contains elements that are both in A & B. The symbol  A ∩ B = {x ǀ x ∈ A, x ∈ B}

For Example –

(i) If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {2, 4, 6, 8, 10, 12, 14, 16}

Then,  A ∩ B = {2, 4, 6, 8}

We can observe that, A ∩ B  ⊆  A  and  A ∩ B  ⊆  B

(ii) If A = {1, 3, 5, 7}, and B = {2, 4, 6, 8}, then these two sets do not have any common members. They are disjoint set . Their intersection is the null set, that is, A ∩ B = ϕ

Two sets A & B are said to be disjoint or mutually exclusive if and only if there is no element common to A & B, i.e., if their intersection is the empty set, i.e., A ∩ B = ϕ

(iii) Let,  A = {2, 4, 6, 8, 9, 10, 12}

B = {1, 6, 7, 10, 11, 12}

C = {2, 5, 8, 12, 15} then

A ∩ B = {2, 4, 6, 8, 9, 10, 12} ∩ {1, 6, 7, 10, 11, 12} = {6, 10, 12}

B ∩ A = {1, 6, 7, 10, 11, 12} ∩ {2, 4, 6, 8, 9, 10, 12} = {6, 10, 12}

So,  A ∩ B = B ∩ A

Now, (A ∩ B) ∩ C{6, 10, 12} ∩ {2, 5, 8, 12, 15} = {12}

Again, B ∩ C = {1, 6, 7, 10, 11, 12} ∩ {2, 5, 8, 12, 15} = {12}

A ∩ (B ∩ C) = {2, 4, 6, 8, 9, 10, 12} ∩ {12} = {12}

So,  (A ∩ B) ∩ C = A ∩ (B ∩ C)

(iv) Let, A = {x ǀ 2x +9 = 0, x ∈ N}, B = {1, 2, 3, 4}

2x + 9 = 0, gives x = - 9/2 which is not a natural number

So,   A = ϕ

Or,   A ∩ B = ϕ ∩ {1, 2, 3, 4} = ϕ Properties Of Intersection Of Sets,