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Question

# A and B are two finite sets, such that A has p elements and B has q elements. The number of elements in the power set of A is 48 more than number of elements in the power set of B. Then select the correct statement about p & q.

A
p=4
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B
p=6
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C
q=6
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D
q=4
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Solution

## The correct option is D q=4Given n(A)=p;n(B)=q Now, Cardianality of power set of any set X having x elements is given as: n(X)=x ⇒n(P(A))=2p;n(P(B))=2q It is given, that 2p=48+2q ⇒2p−2q=48 ⇒2q(2p2q−1)=48 ⇒2q(2p−q−1)=48 ⇒2q(2p−q−1)=24(22−1) Comparing, we get: q=4;p=q+2=6

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