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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 $m \cdot n$ is _______.
$2^m = 112 + 2^n \Rightarrow 2^m - 2^n = 112$
$\Rightarrow 2^n(2^{m-n} - 1) = 2^4(2^3 - 1)$
$\therefore m = 7, n = 4 \Rightarrow mn = 28$
BETA
