Question

The power set of $\{0,1,2\}$ is_____.

• A. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\{\varphi ,\{1\},\left\{2\right\},\left\{0\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\},\left\{0,1,2\right\}\}$
• B. $\{\varphi ,\{1\},\left\{2\right\},\left\{0\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\}\}$
• C. $\{\varphi ,\{1\},\left\{0\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\},\left\{0,1,2\right\}\}$
• D. $\left\{\{1\right\},\left\{2\right\},\left\{0\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\},\left\{0,1,2\right\}\}$
  

Answer 1

The correct option is A <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\{\varphi ,\{1\},\left\{2\right\},\left\{0\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\},\left\{0,1,2\right\}\}$

The power set of any set $S$ is the set of all subsets of $S$.
Consider $S=\{0,1,2\}$
Note that empty set is a subset of every set and every set is a subset of itself.
Also, $\left\{1\right\}$ ,$\left\{2\right\}$,$\left\{0\right\}$ ,$\{0,1\}$ ,$\{0,2\}$ and $\{1,2\}$ are subsets of $S$ .
$⟹\text{The power set of S},P\left(S\right)=\{\varphi ,\{1\},\left\{2\right\},\left\{0\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\},\left\{0,1,2\right\}\}$