I have some home work with problems such as...
Determine whether each of these sets is the power set of a set:
$ 1. \{\phi, \{a\}\}$
$ 2. \phi$
So yes $1$ is the power set of $\{a\}$.
But what about $2?$ Since power sets have to have $2^k$ members then no it can't be a power set. It would have to be $P(\phi) = \{\phi, \{\phi\}\}$ correct? Since it must contain $2$ members. However, when I try to check myself with Wolfram Alpha, it says $P(\{\}) = \{\{\}\}...$ why? I thought it must have $2^k$ members!