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(C) Let set $A$ have $m$ elements and set $B$ have $n$ elements. The number of subsets of set $A$ is $2^m$ and the number of subsets of set $B$ is $2^

Vedclass · Accepted Answer

$6, 3$

Vedclass · Answer

(C) Let set $A$ have $m$ elements and set $B$ have $n$ elements. The number of subsets of set $A$ is $2^m$ and the number of subsets of set $B$ is $2^n$. According to the problem,$2^m - 2^n = 56$. We can write this as $2^n(2^{m-n} - 1) = 56$. Factorizing $56$,we get $56 = 8 	imes 7 = 2^3 	imes (2^3 - 1)$. Comparing $2^n(2^{m-n} - 1) = 2^3(2^3 - 1)$,we get $n = 3$ and $m - n = 3$. Substituting $n = 3$ into $m - n = 3$,we get $m - 3 = 3$,which implies $m = 6$. Thus,the values of $m$ and $n$ are $6$ and $3$ respectively.

Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$,respectively are

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