Question

Write down the power set of set $B=\{1,2,3\}$.

Answer 1

Power set.

A power set consists of all subsets, the empty set, and the original set.

i.e; Total number of power set $=2^{\mathrm{n}}$ where $\mathrm{n}$ is the number of elements is the given set

Given set is, $B=\left\{1,2,3\right\}$ here $\mathrm{n}=3$

So, the Total number of power set $=2^{\mathrm{n}}=2^3=8$

Thus, Subsets of the set $B=\left\{1,2,3\right\}$ are $\varphi ,\left\{1\right\},\left\{2\right\},\left\{3\right\},\{1,2\},\{1,3\},\{2,3\}$ and$\{1,2,3\}$.

Hence, the power set of the set $B$ is $\left\{\varphi ,\left\{1\right\},\left\{2\right\},\left\{3\right\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\right\}$.