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

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?

Answer
It is given that
n(X) = 8, n(Y) = 15 and n(X ∪ Y) = 18, find n(X ∩Y)
Use formula
n ( X ∪ Y ) = n ( X ) + n ( Y ) – n ( X ∩ Y )
Plug the values we get
18 = 8 + 15 - n ( X ∩ Y )
n ( X ∩ Y ) = 23 – 18 = 5
Answer is n(X ∩Y) = 5