Question

If $A=\left\{x,y\right\}$, then the power set of $A$ is

• A. $\left\{x^x,y^y\right\}$
• B. $\left\{ɸ,x,y\right\}$
• C. $\left\{ɸ,\left\{x\right\},\left\{2y\right\}\right\}$
• D. $\left\{ɸ,\left\{x\right\},\left\{y\right\},\left\{x,y\right\}\right\}$

Answer 1

The correct option is D

$\left\{ɸ,\left\{x\right\},\left\{y\right\},\left\{x,y\right\}\right\}$

Explanation for the correct option:

Given, $A=\left\{x,y\right\}$

Power set $=$Set of all possible subsets of $A$

$\mathbf{\therefore }\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\left\{\varphi ,\left\{x\right\},\left\{y\right\},\left\{x,y\right\}\right\}$

Hence, Option ‘D’ is Correct.