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# The no. of subsets of a finite set A is 56 more than the no. of subsets of another finite set B. What is the no. of elements of A?

$\begin{array}{1 1} 5 \\ 6 \\ 7\\ 8 \end{array}$

Toolbox:
• No. of of subsets of a set having n elements =$2^n$
Let n(A)=n and n(B)=m
$2^n=56+2^m$
$\Rightarrow\:2^n-2^m=56$
$\Rightarrow$ n=6 and m=3
$\Rightarrow\:$No. of elements of A=6
edited May 17, 2014