Question

The total number of subsets of a set A is 120 more than the total number of subsets of set B. The number of elements in the two sets respectively are

(A) 3, 7 (B) 4, 8 (C) 8, 4 (D) 7, 3

Answer 1

(D) 7, 3

Explanation:

If a set has 'n' elements, the total number of subsets is (2^n) - 1

So if set A has more subsets than set B, it needs to have more elements, so option (A) and (B) can't be correct.

So, checking option (C), we have:

Set A: number of subsets = 2^8 - 1 = 255

Set A: number of subsets = 2^4 - 1 = 15

Difference: 255 - 15 = 240

The difference is not 120, so this is not the correct option

Option (D):

Set A: number of subsets = 2^7 - 1 = 127

Set A: number of subsets = 2^3 - 1 = 7

Difference: 127 - 7 = 120

Correct option: (D)