Question

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power in power set of the second set. Then, the values of m and n are:

 A. 7, 6 

B. 6, 8 

C. 6, 4 

D. 7, 4

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) ) + 48 

⇒ 2m = 2n + 48

Above equation is only true when m = 6 and n = 4