Question

Two finite ets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of ma and n are respectively.

• A. 4,7
• B. 7,4
• C. 4,4
• D. 7,7

Answer 1

The correct option is A

4,7

Since number of subsets of a set containing m elements is 112 more than the subsets of the set containing n elements.

$\because 2^m-2^n=112$

$\Rightarrow 2^n.(2^{m-n}-1)=2^4.7$

$\Rightarrow 2^n=2^{4}and{2}^{m-n}-1=7$

$\Rightarrow n=4and{2}^{m-n}=8$

$\Rightarrow 2^{m-n}=2^3\Rightarrow m-n=3$

$\Rightarrow m-4=3m=4+3$

$\therefore m=7$