The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in set A? (1) 5 (2) 6 (3) 7 (4) 8

Solution: (2)

Let the number of elements in set A be p and set B be q.

The power set of A is P (A) and B is P (B).

P (A) has 2p elements and P (B) has 2q elements. 

2p – 2q = 56

2q [2p-q – 1] = 8 * 7 = 23 [23 – 1] 

2q [2p-q – 1] = 23 [23 – 1]

q = 3, p – q = 3

p – 3 = 3

p = 3 + 3 = 6

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