Question

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

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

Answer 1

Answer: (C)

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

To find power set of A, we have to find subsets of set A.

There are four subsets of set A-

1. $\varphi$

2. $\left(\varphi \right)$

3. $\left\{\left(\varphi \right)\right\}$

4. $\{\varphi ,\left\{\left(\varphi \right)\right\}\}$

Thus, power set of set A is,

$P\left(A\right)=\{\varphi ,\left(\varphi \right),\left\{\left(\varphi \right)\right\},\{\varphi ,\left\{\left(\varphi \right)\right\}\}\}$