Answer :

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

According to the question,

2^{m} – 2^{n} = 56

⇒ 2^{n} (2^{m-n} – 1) = 56

⇒ 2^{n} (2^{m-n} – 1) = 8× 7

⇒ 2^{n} (2^{m-n} – 1) = 2^{3} × (2^{3} – 1)

⇒ n = 3, m-n = 3

⇒ m-3 = 3

⇒ m = 6

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