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Power Set

The number of...

Question

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

A

3

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B

16

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C

8

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D

64

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Solution

The correct option is C $8$
Given:
$A = {x : x \in W and x^{3} - 1 \leq 7}$
Now,
$x^{3} - 1 \leq 7$
$\Rightarrow x^{3} \leq 8$
$\Rightarrow x \in (- \infty, 2]$
As $x \in W$ , so
$A = {0, 1, 2} \Rightarrow n (A) = 3 ∴ n (P (A)) = 2^{3} = 8$

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