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Question

If nA denotes the number of elements in set A and if nA=4, n(B)=5 and n(AB)=3, then n(A×B)(B×A)=


A

8

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B

9

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C

10

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D

11

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Solution

The correct option is B

9


Explanation for the correct option

Given that nA=4, n(B)=5 and n(AB)=3

For any given sets P and Q, we know that P×QQ×P=PQ×QP

Therefore, A×BB×A=AB×BA

nA×BB×A=nAB×BA=nAB×nBAnP×Q=nP×nQ=nAB×nABAB=BA=3×3nA×BB×A=9

Hence, the correct option is option(B) i.e. 9


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