Question

Two finite sets have \(m\) and \(n\) elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of \(m\) and \(n\) respectively are.
(A) 7,6 (B) 5,1 (C) 6,3 (D) 8,7

Answer 1

The correct answer Is (C).
Since, let \(A\) and \(B\) be such sets, i.e., \(n(A)=m, n(B)=n\)
So \(n(P(A))=2^{m}, n(P(B))=2^{n}\)
Thus \(n(P(A))-n(P(B))=56\), i.e., \(2^{m}-2^{n}=56\)
\(=2^{n}\left(2^{m-n}-1\right)=2^{3} 7\)
\(=n=3,2^{m-n}-1=7\)
\(=m=6\)

Answer 2

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