Question

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are:

• A. 7, 6
• B. 6, 3
• C. 5, 1
• D. 8, 7

Answer 1

Answer: (B)

Given: Two finite sets have $m$ and $n$ elements
$\therefore 2^{ m }-2^{ n }=56$
$ \Rightarrow 2^{ m }-2^{ n }=64-8$
$\Rightarrow 2^{m}-2^{n}=2^{6}-2^{3} $
$\Rightarrow m=6, n=3$