Suppose that f is a function from the set A to the set B.
Chapter 2, Problem 16E(choose chapter or problem)
Suppose that f is a function from the set A to the set B. Prove thata) if f is one-to-one, then Sf is a one-to-one function from p(A) to p(B).________________b) if f is onto function, then Sf is an onto function from p(A) to p(B).________________c) if f is onto function, then Sf?1 is a one-to-one function from p(B) to p(A).________________d) if f is one-to-one, then Sf is an onto function from p(B) to p(A).________________e) if f is a one-to-one correspondence, then Sf is a one- to-one correspondence from p(A) to p(B) and Sf?1 is a one-to-one correspondence from p(B) to p(A). [Hint: Use parts (a)-(d).]
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