Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than that of the total no. of subsets of the second set. Find the values of m and n.

We have m elements in the first set.

When forming the subset each element has choices; to either get selected or not.

So, each of these m elements has 2 choices.

Therefore, total possible selections from first set = 2^{m}

Similarly,** **total possible selections from second set = 2^{n} Hence, 2

^{m}– 2

^{n}= 56

This is only true when 64 – 8 = 56.

or 2^{6} – 2^{3} = 56

Therefore m = 6 and n = 3

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