If the empty set is a subset of all sets, why isn't it a member of every subset of a power set? If $s=\{1,2\}$, then we say that $P(s) = \{\{\},\{1\},\{2\},\{1,2\}\}$.
But the power set is the set of all subsets, of which $\{\}$ is one of them. So why doesn't the power set also include sets such as $\{\{\},1\}$, $\{\{\},2\}$, and $\{\{\},1,2\}$?

The empty set is not a member of the set in question. In much the same way, the set is not a member of the set, so the powerset doesn't include $\{2,\{1,2\}\}$
