If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

Question

Philoid · Accepted Answer

Given-

n(X) = 40, n(X ∩ Y) = 10, and n(X ∪ Y) = 60

We know that-

n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)

⇒ 60 = 40+n(Y) - 10

⇒ 60 = 30+n(Y)

⇒ n(Y) = 60-30

∴ n(Y) = 30

Thus, the no. of elements in n(Y) is 30.