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  • Two finite sets have m and n elements. The total number subsets of first set is 56 more than second set, find m and n.

Two finite sets have m and n elements. The total number subsets of first set is 56 more than second set, find m and n.

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best_answer

Total number of subset having n elements = \small 2^{k}, where k is the number of element in the set

Let two sets be M and N with m and n elements respectively &

according to question

\small \therefore  \small 2^{m}=2^{n}+56

where,

\small 2^{m} =total  number of subsets of M\\

\small 2^{n} =total number of subsets of N\\

 \small 2^{m}-2^{n}=56\\ 2^{n}(2^{m-n-1}-1)=2^{3}(2^{3}-1)\\ therefore,\\ n=3 ,\: m-n=3\\ m=6

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Rakesh

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