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

 We know, if any set has $m$ elements, then the number of subsets is $2^m$.

$\therefore$According to the given condition, we have 

$2^m -2^n = 112=16 \times 7 \Rightarrow 2^{m }-2^n = 2^{7 }- 2^4$

On comparing both sides, we get  $m =7$ and $n=4$