If X and Y are two sets such that n (X) = 17, n (Y) = 23 and n ( X ∪ Y ) = 38, find n ( X ∩ Y ).

Question

Philoid · Accepted Answer

Given-

n(X) = 17, n(Y) = 23, and n(X ∪ Y) = 38

We know that-

n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)

⇒ 38 = 17+23 - n(X ∩ Y)

⇒ 38 = 40 - n(X ∩ Y)

⇒ n(X ∩ Y) = 40-38

∴ n(X ∩ Y) = 2