Suppose f: A --> B is a function. Define the function F: P(B) --> P(A) (from the powerset of B to the one of A) by setting F(S) = f-1(S) for all S subset of B. Prove or disprove: (1) F is 1-1 if and only if f is onto.  (2) F is onto if and only if f is 1-1.  [Finite, not infinite.

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