Let X = ( \ {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.

Let X = ℤ × (ℤ {0}). Define the relation on X by(x, y) (z, t) ↔ xt = yzfor every (x, y), (z, t) ∈ X.(a) Show that this is an equivalence relation on X. 4 marks(b) Find the equivalence classes of (0, 1) and of (3, 3). 4 marks(c) Show that if (x, y) ≡ (x', y') and (z, t) ≡ (z', t') then (xt + yz, yt) ≡ (x't' + y'z', y't').