Question

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

Options

• m = 3, n = 6

• m = 6, n = 3

• m = 5, n = 6

• None of these

Answer 1

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then m = 6, n = 3.

Explanation:

2^m = 2ⁿ + 56

`\implies` 2^m – 2ⁿ = 64 – 8 = 2⁶ – 2³