If A={ϕ,{ϕ}} then the power set of A is

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

1. A

A

2. B

$\left\{\mathrm{\varphi },\left\{\mathrm{\varphi }\right\},\mathrm{A}\right\}$

3. C

$\left\{\mathrm{\varphi },\left\{\mathrm{\varphi }\right\},\left\{\left\{\mathrm{\varphi }\right\}\right\},\mathrm{A}\right\}$

4. D

None of these

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### Solution:

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

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

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

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