Question

Assertion :The power set of a set $A$ contains $128$ elements then number of elements in set $A$ are $7$. Reason: Number of subsets of a set $A$ having $n$ elements is equal to $2^n$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

If $A=\{1,2,\mathrm{3...}n\}$

$\therefore$ Number of subsets of $A=2^n$
$\therefore 2^n=128$ ( $\because$ Power set is the set of all subsets of $A$)

or $2^n=2^7$
$\therefore$ Number of elements in sets $A=$7

$\therefore$ Assertion $\left(A\right)$ and Reason $\left(R\right)$ both are correct and Assertion is correctly explained by Reason