Q2 of 71 Page 30

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?

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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i. List U, G and H


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U = {5, 6, 7, 8, 9, 10, 11, 12, 13}


M = {5, 8, 10, 11},


N = {5, 6, 7, 9, 10}

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If n(A ∩ B) = 5, n(A ∪ B) = 35, n(A) = 13, find n(B).