Question

Let $P\left(S\right)$ denote the power set of a set $S$. Which of the following is always true ?

• A. $P\left(P\right(S)=P(S)$
• B. $P\left(S\right)\cap P\left(P\right(S\left)\right)=\left\{\varphi \right\}$
• C. $P\left(S\right)\cap S=P\left(S\right)$
• D. $S\text{/}ϵP\left(S\right)$

Answer 1

The correct option is B $P\left(S\right)\cap P\left(P\right(S\left)\right)=\left\{\varphi \right\}$

$\varphi$ always present in any powerset of a set and $\varphi$ is the only common element between $P\left(S\right)$ and $P\left(P\right(S\left)\right)$
$\therefore P\left(S\right)\cap P\left(P\right(S\left)\right)=\left\{\varphi \right\}$