Solve this following

Question:

Set A has m elements and Set B has n elements. If the total number of subsets of $\mathrm{A}$ is 112 more than the total number of subsets of B, then the value of $m . n$ is..

 

Solution:

$2^{m}-2^{n}=112$

$\mathrm{m}=7, \mathrm{n}=4$

$\left(2^{7}-2^{4}=112\right)$

$\mathrm{m} \times \mathrm{n}=7 \times 4=28$

 

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