4. Let be an relation a A write [a] to denote the equivalence class of a with respect to. Given a, b = A, show that the following are equivalent: equivalence on a set A, and for each (1) [a] = [b] (2) a = b (3) a [b] (4) [a] [b] (5) b = a (6) b = [a] (7) [b] [a] (8) [a]n[b] = 0.