The number of elements of the power set of a set containing n elements is

Options

A. `2^(n-1)`
B. `2^(n)`
C. `2^(n)-1`
D. `2^(n+1)`

Answer

B

Explanation

Let set A contains n elements.
Power set of a is the set of all subsets.
`therefore` Number of subsets of `A=.^(n)C_(o)+.^(n)C_(1)+.^(n)C_(2)+...+.^(n)C_(n)=2^(n)`
`therefore` Power set of A contains `2^(n)` elements.