Empty sets befuddle me. I have a series of questions dealing with an empty set and unsure if any of them are correct. I'll need to type up the questions and my thoughts below, if someone could verify or help show my why they are wrong.

Question

anonymous · Answer

True of False?
$$\emptyset \subseteq \{\emptyset\}$$
True, if we consider the power set of the empty set, then the empty set would be a subset of it.

$$\emptyset \in \emptyset$$
I... don't even know. I would say know simply based off the fact I'm saying yes to the next.

$$\emptyset \in \{\emptyset\}$$
True, again, considering the power set of the empty set contains the element the empty set, it would be true.

kinggeorge · Answer

You're absolutely correct on all three counts. $\emptyset$ is a subset of every set, and it's clearly an element in $\{\emptyset\}$. As for the second one, $\emptyset$ has no elements, so can not contain $\emptyset$.

anonymous · Answer

Great! Thank you for your help!

kinggeorge · Answer

No problem.