The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in the set A?

Options

A. 5
B. 6
C. 7
D. 8

Answer

B

Explanation

Let sets A and B have m and n elements, respectively.
Then, `2^(m)-2^(n)=56implies2^(n)(2^(m-n)-1)=56`
`implies2^(n)(2^(m-n)-1)=8xx7implies2^(n)(2^(m-n)-1)=2^(3)xx7`
On comparing both sides, we get
`2^(n)=2^(3)" and "2^(m-n)-1=7`
`implies" "n=3" and "2^(m-n)=8`
`implies" "2^(m-n)=2^(3)impliesm-n=3`
`implies" "m-3=3impliesm=6`
Hence, number of the elements in set A is 6.