Question

The power set of $\{1,2\}$ is

• A. $\left\{1\right\},\left\{2\right\}$
• B. $\left\{\right\{1\},\{2\},\{1,2\left\}\right\}$
• C. $\{1,2\}$
• D. $\{\varnothing ,\{1\},\{2\},\{1,2\left\}\right\}$

Answer 1

The correct option is D $\{\varnothing ,\{1\},\{2\},\{1,2\left\}\right\}$

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