2.6 Equivalence relation 1. Equivalence relation Definition 2.18: A relation r on a set a is called an equivalence relation if it is reflexive symmetric, and transitive. Example: Let m be a positive integer with m>l Show that congruence modulo m is an equivalence relation. R=(a, b )la=b mod m) Proof: (Reflexive (for any aEZ, aRa?) 2)symmetric (for any arb, bRa?) transitive(for arb, bRc, arc?)2.6 Equivalence Relation 1.Equivalence relation Definition 2.18: A relation R on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive. Example: Let m be a positive integer with m>1. Show that congruence modulo m is an equivalence relation. R={(a,b)|ab mod m} Proof: (1)reflexive (for any aZ，aRa?) (2)symmetric (for any aRb， bRa?) (3)transitive (for aRb，bRc，aRc?)