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Question

# For two finite disjoint sets A and B, if the number of elements in power set of A is 224 more than the number of elements in power set of B, then the number of elements present in either of the sets is

A
12
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B
0
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C
15
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D
13
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Solution

## The correct option is D 13Let n(A)=x and n(B)=y (x>y) Number of elements in P(A) i.e., n(P(A))=2x and n(P(B))=2y Given that 2x−2y=224 ⇒2y(2x−y−1)=32×7⇒2y(2x−y−1)=25(23−1) On comparison, we get y=5, x−y=3⇒x=8 Since A and B are disjoint, ∴A∩B=ϕ⇒n(A∩B)=0 Hence, n(A∪B)=n(A)+n(B)=13

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