Supoose that we want to enumerate the elements contained in the below sets
(a) $\emptyset$ , (b) $\{\emptyset\}$ , (c) $\{\{\emptyset\}\}$, (d) $\{\emptyset, \{\emptyset\}\}$
The question is simple. How many elements contain each set?
My solution: The first set is the empty set so it contains 0 elements. The second set contains an empty set, consequently, contains 1 element. The third one contains 1 element because contains a set which set contains the empty set. Finally, the last one contains 2 elements. The empty set and the set that contains an empty set. Is this solution correct ?
My mind bleeds !!!