Q15 of 71 Page 30

A and B are two sets such that n(A – B) = 32 + x, n (B – A) = 5x and n(A B) = x Illustrate the information by means of a Venn diagram. Given that n(A) = n(B). Calculate (i) the value of x (ii) n(A B).

Given that


n(A–B) = 32 + x


n(B–A) = 5x


n(A∩B) = x


and n(A) = n(B)


using these results


n(A) = n(A–B) + n(A∩B)


n(B) = n(B–A) + n(A∩B)


n(A∪B) = n(A–B) + n(A∩B) + n(B–A)


But given that n(A) = n(B)


So, n(A–B) + n(A∩B) = n(B–A) + n(A∩B)


n(A–B) = n(B–A)


32 + x = 5x


5x–x = 32


4x = 32


(i) x = 32/4 = 8


(ii) n(A∪B) = n(A–B) + n(A∩B) + n(B–A)


= 32 + x + x + 5x


= 32 + 7x


= 32 + 7(8)


= 88


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