Question

If A is a void set then n[P(P(P(A)))] is

• A. 0
• B. 1
• C. 3
• D. 4

Answer 1

The correct option is D 4

No. of elements in $A$ is $0$.

Hence $n\left(P\right(A\left)\right)=2^0=1$

$P\left(A\right)$ has 1 element.

Hence $n\left(P\right(P\left(A\right)\left)\right)=2^1=2$

$P\left(P\right(A\left)\right)$ has 2 elements.

Hence $n\left(P\right(P\left(P\right(A\left)\right)\left)\right)=2^2=4$