If A and B are 2 sets such that A U B has 40 elements, A has 18 elements and B has 29 elements, how many elements does A ∩ B have? __

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Solution

Since n(A U B) = n(A) + n(B) - n(A ∩ B)

Given : n(A U B) =40, n(A) =18, n(B) =29

Hence, n(A ∩ B) = n(A) + n(B) - n(A U B)

= 18 + 29 - 40

= 7

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