# 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

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.n is ___

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Explaination:

No. of subsets of A=2m
No. of subsets of B=2n
2m=2n+112
2m−2n=112

2n(2m−n−1)=112
2n(2m−n−1)=24(23−1)
n=4
m−n=3
m−4=3
⇒m=7
m×n=28
=28