Question

The power set of $\left\{9\right\}$ is________.

• A. $\{\varphi ,\{0\},\{9\left\}\right\}$
  
• B. $\left\{9\right\}$
  
• C. $\left\{\varphi \right\}$
  
• D. $\{\varphi ,\{9\left\}\right\}$
  

Answer 1

The correct option is D $\{\varphi ,\{9\left\}\right\}$


The power set of any set $S$ is the set of all subsets of $S$.
Consider $S=\left\{9\right\}$
Note that empty set is a subset of every set and every set is a subset of itself.

$⟹\text{The power set of S},P\left(S\right)=\{\varphi ,\{9\left\}\right\}$