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?

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?

Answer
It is given that
n(X) = 40, n(X ∪ Y) = 60 and n(X ∩ Y) = 10
Use the formula
n(X ∪ Y) = n(X) + n(Y) - n(X ∩ Y)
Plug the values, we get
⇒ 60 = 40 + n(Y) - 10
⇒60 = 30 + n(Y)
⇒n(Y) = 60 - 30 = 30
Hence, the set Y has 30 elements.