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

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

Answer
Use formula
n ( X ∪ Y ) = n ( X ) + n ( Y ) – n ( X ∩ Y )
Plug the values we get
38 = 17 + 23 - n ( X ∩ Y )
n ( X ∩ Y ) = 40 – 38 = 2
Answer is n(X ∩Y) = 5