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 $2^{2^n}$

$N\left(P\right(A\left)\right)=2^n$

If a set having n numbers elements

$N\left(P\right(A\left)\right)=2^{2^n}$

So $P\left(P\right(A\left)\right)=2^{2^n}$