chapter 8 THE DISJOINT SET ADT 81 Equivalence relations Definition) Arelation R is defined on a set S if for every pair of elements(a, b),a, b ES, aR b is either true or false. If a b is true, then we say that a is related to b Definition A relation, over a set, S, is said to be an equivalence relation over S iff it is symmetric, reflexive, and transitive over S (Definition Two members x and y of a set S are said to be in the same equivalence class iffx-yCHAPTER 8 THE DISJOINT SET ADT §1 Equivalence Relations 【Definition】A relation R is defined on a set S if for every pair of elements (a, b), a, b S, a R b is either true or false. If a R b is true, then we say that a is related to b. 【Definition】A relation, ~, over a set, S, is said to be an equivalence relation over S iff it is symmetric, reflexive, and transitive over S. 【Definition】Two members x and y of a set S are said to be in the same equivalence class iff x ~ y