Theorem 4.6 Let S be a nonempty set. a) Let R be an equivalence relation on S. For any two members x and y of S. define x y provided that x and y belong to the same member of S/R. Then xy if and only if x Ry. b) Leto be a partition of S. For any two members x and y of S, define x = y provided that x and y belong to the same member of . Then = {[s]:se S}.