Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of mn is

28 26 30 32

28

The correct answer is Option (1) → 28 It is given that $2^m = 2^n +112$ $⇒2^m-2^n =112$ $⇒2^n(2^{m-n}-1)=16×7$ $⇒2^n (2^{m-n}-1) = 2^4 (2^3-1)$ $⇒n=4$ and $m-n=3⇒ n=4, m =7⇒ mn = 28$