9. Given a function f : Z - Z and a natural number n, we say that f descends to a function modulo n if for all a, be Z, a = b (mod n) implies that f(a) = f(b) (mod n). (NOTE: this is the same as saying that f determines a function on the equivalence classes mod n). (a) Prove or disprove: There is a function f : Z - Z which descends to a function modulo 3 but does not descend to a function modulo 5. (b) Prove or disprove: If f : Z -> Z descends to a function modulo 3 and f descends to a function modulo 2, then f descends to a function modulo 6. (c) Prove or disprove: There is a function f : Z - Z which does not descend to a function modulo n for any n > 2