null empty set has 2 subsets?

Question

The question in the book was:

How many subsets does $\{\emptyset\}$ have?

a) 0, b) 1, c) 2, d) 3.

The answer was c. How can an empty set have 2 subsets?

Answer 1

The subsets of $\{a\}$ are $\{\}=\varnothing$ and $\{a\}$, no matter what $a$ is. Here, we simply have $a=\varnothing$.

On the other hand, if the question asked you for the subsets of $\varnothing$, you'd only have one subset.

REMEMBER THAT $\{\varnothing\}\ne\varnothing$!!