Empty Sets question I need some help understanding empty sets being elements vs subsets to another set.
This ask if it is true or false.
{{∅}} ∈ {∅,{∅}}
{{∅}} ⊆ {∅,{∅}}
I know that they are both false but could someone explain how so?

$\{\emptyset,\{\emptyset\}\}$ has precisely two elements, $\emptyset$ and $\{\emptyset\}$, but $\{\{\emptyset\}\}$ is not one of them. So $\{\{\emptyset\}\}\notin \{\emptyset,\{\emptyset\}\}$.
On the other hand, each element of $\{\{\emptyset\}\}$ (that is, its only element $\{\emptyset\}$) is an element of $\{\emptyset,\{\emptyset\}\}$.
So $\{\{\emptyset\}\}\subseteq \{\emptyset,\{\emptyset\}\}$.
