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?

Question

Philoid · Accepted Answer

Given-

n(X) = 8, n(Y) = 15, and n(X ∪ Y) = 18

We know that-

n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)

⇒ 18 = 8+15 - n(X ∩ Y)

⇒ 18 = 23 - n(X ∩ Y)

⇒ n(X ∩ Y) = 23-18

∴ n(X ∩ Y) = 5