Q. 24.5( 2 Votes )

# If A and B are two sets such that A has 50 elements, B has 65 elements and A ∪ B has 100 elements, how many elements does A ∩ B have?

Answer :

Given, n(A) = 50, n(B) = 65 and n(A ∪ B) = 100.

We have, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

100 = 50 + 65 – n(A ∩ B)

n(A ∩ B) = 50 + 65 – 100 = 115 – 100 = 15

So, A ∩ B has 15 elements.

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