Question

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively. 

A. 4, 7 

B. 7, 4 

C. 4, 4 

D. 7, 7

Answer 1

Let A and B be the set which contain m and n elements respectively. 

Then n(P(A)) = 2^m and n(P(B)) = 2ⁿ 

Also given that,n(P(A)) = n(P(B) )+112 

⇒ 2^m = 2ⁿ +112 

Above equation is only true when m =7 and n = 4.