Recall that we define [5 pts] zn = {[0],−1]} to be the set of congruence classes modulo n. also define the function fn : zn →zn, f(x) = x2. for example, z11 = {[0],[1],}, and f11([5]) = [3], since 52 = 25 ≡ 3 (mod 11). (a) create a table showing all input-output pairs for the function f11 : z11 →z11. (b) show that f11 is neither surjective nor injective. (c) show that fn is never injective for integer n ≥ 3. (hint: consider what happens to the congruence classes [1] and [n−1].)