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

Solution:

Given n(X) = 17

n(Y) = 23

n(X⋃Y) = 38

n(X∪Y) = n(X) + n(Y) – n(X∩Y)

38 = 17 + 23 – n(X∩Y)

38 = 40 – n(X∩Y)

=> n(X∩Y) = 2

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