Determine Whether the Given Set Is the Power Set of Some

Short Answer

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.
- $$\begin{array} { c } \{ \emptyset , \{ \emptyset \} , \{ a \} , \{ \{ a \} \} , \{ \{ \{ a \} \} \} , \{ \emptyset , a \} , \{ \emptyset , \{ a \} \} , \{ \emptyset , \{ \{ a \} \} \} , \{ a , \{ a \} \} , \{ a , \{ \{ a \} \} \} , \{ \{ a \} , \{ \{ a \} \} \} , \\\{ \emptyset , a , \{ a \} \} , \{ \emptyset , a , \{ \{ a \} \} \} , \{ \emptyset , \{ a \} , \{ \{ a \} \} \} , \{ a , \{ a \} , \{ \{ a \} \} \} , \{ \emptyset , a , \{ a \} , \{ \{ a \} \} \} \}\end{array}$$