The powerset of {0,1} is {{},{0},{1},{0,1}}. The answer to this problem says that {{0}}, {}, {{}}, are subsets of the powerset, but {0} is not a subset of the powerset.
However, this doesn't make any sense to me. Obviously {0} and {} are the only ones in the powerset and nothing else is in the powerset. What is the solution talking about?
{0} is an element from the power set, so {{0}} (a box containing the element {0}) is a subset of the powerset, but {0} itself is not.