Question

Two finite sets have m and n elements, respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. What are the values of m and n, respectively? 

(a) 7, 6 

(b) 6, 3 

(c) 5, 1

(d) 8, 7

Answer 1

Correct option is (b) 6,3

Explanation:

Let n(A) = m, n(B) = n 

The total possible subsets of A and B are 2^m and 2ⁿ, 

respectively. 

According to the given condition, 

2^m - 2ⁿ = 56

⇒ 2ⁿ (2^{m - n} - 1) = 2³ (2³ - 1) 

⇒ n = 3, m - n = 3  ⇒ m = 6, n = 3