Is {{∅}} ⊂ {{∅},{∅}} true or false. I can't decide if this question is true or false. It seems to be false as the sets would be equal? is that correct since an proper subset isn't equal.
the ⊂ in this means proper subset, the answer is false thanks to the below response.
Best Answer
Both sets are the same.
The only element in $\{\{\emptyset\}\}$ is $\{\emptyset\}$, and the elements in $\{\{\emptyset\},\{\emptyset\}\}$ are $\{\emptyset\}$ and $\{\emptyset\}$, thus it has only one element, $\{\emptyset\}$.
If $\subset$ denotes proper and not equal subset, it is false.
If $\subset$ denotes proper or equal subset, it is true.