If $\mathrm{A}=\{\mathrm{\varphi },\{\mathrm{\varphi }\left\}\right\}$ then the power set of A is

Solution:

we have, $\mathrm{A}=\{\mathrm{\varphi },\{\mathrm{\varphi }\left\}\right\}$

Subset of set A are $\mathrm{\varphi },\left\{\mathrm{\varphi }\right\},\left\{\right\{\mathrm{\varphi }\left\}\right\},\{\mathrm{\varphi },\{\mathrm{\varphi }\left\}\right\}$
.'. Power set of A i.e.

$\begin{array}{r}\mathrm{P}\left(\mathrm{A}\right)=\{\mathrm{\varphi },\{\mathrm{\varphi }\},\{\left\{\mathrm{\varphi }\right\}\},\{\mathrm{\varphi },\left\{\mathrm{\varphi }\right\}\left\}\right\}\\ \Rightarrow \mathrm{P}\left(\mathrm{A}\right)=\{\mathrm{\varphi },\{\mathrm{\varphi }\},\{\left\{\mathrm{\varphi }\right\}\},\mathrm{A}\}\end{array}$