Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$? $\{\emptyset\}$ is a set containing the empty set. Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?

My hypothesis is yes by looking at the form of "the superset $\{\{\emptyset\}\}$" which contains "the subset $\{\emptyset\}$".
It's easier to just replace everything by variables, then it's clearer.

Set $a=\varnothing, b=\{\varnothing\}=\{a\}$ and $c=\{\{\varnothing\}\}=\{\{a\}\}=\{b\}$.

Now the question is whether or not $\{a\}\subseteq\{b\}$. But since $a\neq b$, it's easy to see that the answer is negative.
Think of {∅} as a box containing an empty box, then
{{∅}} is a box containing a box which contains an empty box, in which case
{{∅}} is box containing {∅}, which means

{∅} is subset of {{∅}}