and I'm still not sure I fully understand it.
Back to my comp. theory classs, I'd say an example would be
X = B* (ie: Null, B, BB, BBB, BBBB, etc).
Y = B*C* (ie: Null, B, C, BC, BBC, BCC, BBCC, etc).
and the premise is for P which returns the set of all prefixes for a given language.
(Oops, we forgot a step, let's say our language is the element = {A, B, C})
The question you are asked to prove is
Given P(X) is a subset of Y, is that equivalent to X is a subset of P(Y).
So, would P(X) == [A|B|C]*B*
and would P(Y) == [A|B|C]*B*C* ?