If X and Y are two sets such that X∪Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X∩Y have?

Given

n (X U Y) = 18

n (X) = 8

n (Y) = 15

We can write it as

n (X U Y) = n (X) + n (Y) – n (X ∩ Y)

Substituting the values

18 = 8 + 15 – n (X ∩ Y)

By further calculation

n (X ∩ Y) = 23 – 18 = 5

So we get

n (X ∩ Y) = 5

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

Prove that A – B = A ∩ B.’

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Prove that A ∩ (A ⋃ B)’ = ϕ

If A = {3, {2}}, find P(A).