Question

Two finite sets have m and n element respectively The total number of subsets of first set is 112 more than the total number of sub sets of the second set The value of m and n respectively are 

(a) 5, 2 

(b) 4, 7 

(c) 7, 4 

(d) 2, 5

Answer 1

The correct option (c) 7, 4

Explanation:

Hence 2^m = 2ⁿ + 112 is given 

⇒ 2ⁿ(2^{m – n} – 1) = 2⁴ x 7 

⇒ n = 4 and 2^{m – n} – 1 = 7 

⇒ n = 4 and 2^m–4 = 8 

⇒ n = 4 and m = 7