Question

Assertion :The number of non empty subsets of the set $\{a,b,c,d\}$ are $15$. Reason: Number of non empty subsets of a set having $n$ elements are $2^n-1$.

• 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

$A=\{a,b,c,d\}$

$\therefore n\left(A\right)=4$

$\therefore$ Number of subset of $A=2^4=16$ out of which only one set is empty set because empty set is subset of every set.

$\therefore$ Number of non empty subset of $A=2^4-1=15$