Question

The number of elements in the power set of $A$, where $A=\{x:x\in W\text{and}{x}^3-1\le 7\}$

• A. $3$
• B. $16$
• C. $8$
• D. $64$

Answer 1

The correct option is C $8$

Given:
$A=\{x:x\in W\text{and}{x}^3-1\le 7\}$
Now,
$x^3-1\le 7$
$\Rightarrow x^3\le 8$
$\Rightarrow x\in (-\infty ,2]$
As $x\in W$, so
$A=\{0,1,2\}\Rightarrow n\left(A\right)=3\therefore n\left(P\right(A\left)\right)=2^3=8$