Let X = Z × (Z {0}). Define the relation on X by (x, y) (z, t) ↔ xt = yz for every (x, y), (z, t) ∈ X.
(a) Show that this is an equivalence relation on X.
(b) Find the equivalence classes of (0, 1) and of (3, 3).
(c) Show that if (x, y) ≡ (x', y') and (z, t) ≡ (z', t') then (xt + yz, yt) ≡ (x't' + y'z', y't').