Define the relation on the set Zx Z, where (a, b) (c, d) if and only if a -d=c-d. (a) [8 Pts] Prove that is an equivalence relation. (b) [4 Pts] Define a function f such that f (a, b) = f(c,d) if and only if (a,b) = (c,d). (c) [4 Pts] List two additional elements in the equivalence class containing class containing (0,0) and then define the equivalence using set-builder notation in simplest form. (d) [4 Pts] List two additional elements in the equivalence class containing (2,3) and then define the equivalence using set-builder notation in simplest form. (e) [4 Pts] Describe the distinct equivalence classes using set-builder notation. Note that you can define a unique one for each x E Z.