Question

Write the power set of $A$, given that $A=\{1,2,3\}$

• A. $\{\{1,2,3\},\{1,2\},\{1,3\},\{2,3\},\left\{1\right\},\left\{2\right\},\left\{3\right\},\left\{\right\}\}$
• B. $\{\{1,2\},\{1,3\},\{2,3\},\left\{1\right\},\left\{2\right\},\left\{3\right\},\left\{\right\}\}$
• C. $\{\{1,2,3\},\{1,2\},\{1,3\},\{2,3\},\left\{1\right\},\left\{2\right\},\left\{3\right\}\}$
• D. none

Answer 1

The correct option is A $\{\{1,2,3\},\{1,2\},\{1,3\},\{2,3\},\left\{1\right\},\left\{2\right\},\left\{3\right\},\left\{\right\}\}$

Power set of a set is the set of all possible sets formed by elements of the given set and it also includes empty set.

$A=\{1,2,3\}$

Number of elements in set $=n\left(A\right)=3$

$\therefore$ Number of elements in power set $=2^{n\left(A\right)}=2^3=8.$

$P\left(A\right)=\left\{\right\{1,2,3\},\{1,2\},\{1,3\},\{2,3\},\{1\},\{2\},\{3\},\{\left\}\right\}$