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  4. Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are:

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Q. Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are:

KEAMKEAM 2003

Solution:

According to the given condition $ {{2}^{m}}-{{2}^{n}}=48 $ This is possible only when $ m=6 $ and $ n=4 $ .