5. For each of the following, prove that the relation is an equivalence relation. Then give information about the equivalence classes as specified: a) The relation ℛ = {(xx, yy) ∈ ℝ × ℝ: (xx − yy) ∈ ℚ } on ℝ. Describe the equivalence classes of 0; 1 2 ; √7. b) The relation = ��(xx, yy), (aa, bb)�: xx2 + yy2 = aa2 + bb2� on ℝ × ℝ . Sketch the equivalence classes of (1, 2); (4, 0). c) The relation = {(xx, yy) ∈ ℝ × ℝ: sin(xx) = sin(yy)} on ℝ. Describe the equivalence classes of 0; ππ 2 ; ππ 4