Question

If $A$ is a empty set then $n\left[P\right(P\left(P\right(A\left)\right)\left)\right]$ is:

• A. $6$
• B. $16$
• C. $2$
• D. $4$

Answer 1

The correct option is D

$4$

Explanation for the correct option:

Given, $A$is an empty set.

$\Rightarrow$No. of elements in $A$ is $0.$
$\begin{array}{rcl}n\left(P\right(A\left)\right)& =& 2^0\\ & =& 1\end{array}$
$P\left(A\right)$ has $1$ element.
$\begin{array}{rcl}& \Rightarrow & n\left(P\right(P\left(A\right)\left)\right)=2^1\\ & =& 2\end{array}$
$P\left(P\right(A\left)\right)$ has $2$ elements.
$\begin{array}{rcl}& \Rightarrow & n\left(P\right(P\left(P\right(A\left)\right)\left)\right)=2^2\\ & =& 4\end{array}$

Hence, option D is correct.