Question

The power set of a singleton set has elements in all.

• A. $1$
• B. $0$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Let us consider an arbitary singleton set, say $A=\left\{a\right\}$.
Since every set is a subset of itself and empty set is a subset of every set, we have $\varphi$ and $A$ to be subsets of $A$.
Also, these are the only subsets of $A$.
Thus, $\text{Power set of A, P(A)}=\{\varphi ,A\}$
$⟹n\left(P\right(A\left)\right)=2$