HI may you help me solve about this question thanks!

Problem (a variant of 3.2.12(d)(e)(f)): Using the fact that R = {(x, y) E Z x Z : 2 divides (x - y) } is an equivalence relation on Z and without reference to Theorem 3.2.2 and 3.2.4 (You cannot use 0 = {x E Z : x is even}, 1 = {x E Z : x is odd}), prove that for all x, y E Z: . (a) If ac = y, then 2 divides (x - y). . (b) If any # 0, then x = y. . (c) If any = 0, then x * y. Hint: Redo the proof for Theorem 3.2.2 for this specific relation