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) = 56`
` Rightarrow 2^(n) (2^(m-n) -1) = 56 `
` Rightarrow 2^(n) (2^(m-n ) -1) = 8xx 7`
` Rightarrow 2^(n) (2^(m-n)-1) = 2^(3) xx 7`
On comparing both sides, we get
` 2^(n) = 2^(3)`
` and 2^(m -n) -1 =7`
` Rightarrow n= 3 and 2^(m-n) =8`
`Rightarrow 2^(m-n) = 2^(3)`
` Rightarrow m-n=3`
` m -3 =3`
m=6
Hence number of the elements in set A is 6.