Question

If A = {1}. How many elements P[P(P(A))] contains ?

Answer 1

If $A=\left\{1\right\}$

Then num of element in $P\left(A\right)=2^1=2$

num of element in $P\left\{P\right(A\left)\right\}=2^2=4$

num of element in $P\left(P\right(P\left(A\right)\left)\right)=2^4=16$