Below is the question asked by Pinter in A Book of Abstract Algebra, Chapter 14 Exercise A6.
I am totally fine with the first part of the question (where we complete the element by element mapping for $h$).
It's the second part, where the reader is asked to show that
$h$ is a homomorphism for any $A$ and $B \backepsilon B \subset A$
that has me a little confused. Is there some implicit operation that is being referenced for power sets? (and when talking about power sets in the context of groups...is this implicit operation the only one?) Further, I am guessing that the operation in $P_A$ is the same operation that is used in $P_B$? Any clarity would be appreciated!