Question

Two finite sets $A $ and$ B $ have m and n elements respectively. If the total number of subsets of $A $ is 112 more than the total number of subsets of $B$, then the value of m is

• A. 7
• B. 9
• C. 10
• D. 12
• E. 13

Answer 1

Answer: (A)

n(A) = m, n(B) = n
$P(A) = 2^m, P(B) = 2^n$
$\therefore 2^m-2^n=112=2\times 2 \times 2 \times 2 \times 7 $
$ \,2^n(2^{m-n}-1)=2^4 \times 7 =2^4(2^3-1)$
$\therefore n=4,m-n=3 \Rightarrow m-4 =3\Rightarrow m=7$.