Q7 of 24 Page 1

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than total number of subsets of the second subset. Find the values of m and n.

Let A and B be the sets having m and n elements. Then number of subsets of set A are 2m and of B are 2n.


According to the question,


2m – 2n = 56


⇒ 2n (2m-n – 1) = 56


⇒ 2n (2m-n – 1) = 8× 7


⇒ 2n (2m-n – 1) = 23 × (23 – 1)


⇒ n = 3, m-n = 3


⇒ m-3 = 3


⇒ m = 6


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