Question

If $A$ be a finite set having n elements and $P\left(A\right)$ is its power set, then total number of subsets of $P\left(P\right(A\left)\right)$ is

• A. $2$${}^n$
• B. $4$${}^n$
• C. $2$${}^{2^n}$
• D. $2$${}^{2n}$

Answer 1

The correct option is C $2$${}^{2^n}$

The set of all subsets of a set is called its Power set.
Number of subsets of a set with $n$ elements is $=2^n$
So, $P\left(A\right)$ has $2^n$ elements.
Similarly, $P\left(P\right(A\left)\right)$ will have $2^{2^n}$ elements