Question

The power set of $C=\left\{\varphi \right\}$ is

• A. $\left\{\varphi \right\}$
• B. $\{\varphi ,\{\varphi \left\}\right\}$
• C. $\left\{\right\{\varphi \left\}\right\}$
• D. $\left\{0\right\}$

Answer 1

The correct option is B $\{\varphi ,\{\varphi \left\}\right\}$

Given $C=\left\{\varphi \right\}$
This means an empty set is an element of set $C.$
Or, $\varphi \in C\Rightarrow \left\{\varphi \right\}\subseteq C$
$\Rightarrow P\left(C\right)=\{\varphi ,\{\varphi \left\}\right\}$