Question

# If A is a finite set, let P(A) denote the set of all subsets of A and n(A) denote the number of elements in A. If for two finite sets X and Y, n[P(X)]=n[P(Y)]+15 then find n(X) and n(Y).

A
n(X)=4;n(Y)=0
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B
n(X)=4;n(Y)=4
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C
n(X)=0;n(Y)=0
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D
n(X)=0;n(Y)=4
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Solution

## The correct option is A n(X)=4;n(Y)=0A set containing n elements has 2n subsets.No. of subsets of X = No. of subsets of Y + 15.No. of subsets of Y must be an odd no. if no. of elements in X is not 0 which obviously it is not. The only case when 2n is odd is when n=0. hence n(Y)=0.n(P(X))=16⇒2n=16⇒n=4

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