I'd really like some help in answering the next question...anything that might help will save my life:

F is defined this way:F:A→BwhereA,B⊂P(N)andP(N) is the power set of the naturals.

LetS,R∈Asuch thatS is a proper subset of R if and only if F(S) is a proper subset of F(R)

My question is to prove whether or not there is an F from P(N)∖N to P(N) which is also a surjective function?