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. The value of m and n is
A. 7, 6
B. 6, 3
C. 5, 1
D. 8, 7

Answer 1

Correct Answer - B
Since, `2^(m)-2^(n)=56=8xx7=2^(3)xx7`
`implies 2^(n)(2^(m-n)-1)=2^(3)xx7`
`implies n=3and2^(m-n)=8=2^(3)impliesn=3andm-n=3`
implies n = 3 and m - 3 = 3 implies n = 3 and m = 6