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

KEAMKEAM 2005

Solution:

According to question, $ {{2}^{m}}-{{2}^{n}}=56 $
$ {{2}^{n}}({{2}^{m-n}}-1)=56 $
This is possible only, if $ m=6 $ and $ n=3 $ .