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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 $n$ respectively are,
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7,4
$2^{m}-2^{n}=112 \Rightarrow 2^{n}\left(2^{m-n}-1\right)=16.7$
$\quad \therefore \quad 2^{n}\left(2^{m-n}-1\right)=2^{4}\left(2^{3}-1\right)$
Comparing we get $n=4$ and $m-n=3$ $\Rightarrow n=4$ and $m=7$
$\quad \therefore \quad 2^{n}\left(2^{m-n}-1\right)=2^{4}\left(2^{3}-1\right)$
Comparing we get $n=4$ and $m-n=3$ $\Rightarrow n=4$ and $m=7$
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