Question

If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X ∩ Y have?

Answer 1

Given; n(X ∪ Y) = 50; n(X) = 28; n(Y) = 32

n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)

⇒ 50 = 28 + 32 – n(X ∩ Y)

⇒ n(X ∩ Y) = 60 – 50 = 10