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?

just replace the symbol for empty set with your favourite letter and regard the brackets as part of the name of the element. 
For the first example the two elements are $x$ and $\{x\}.$ But the RHS is neither of these since it is $\{\{x\}\}.$ So it is not in the set. 
