... relation on A whose equivalence classes are exactly the sets Ai, i ∈ I.Lecture Notes on Discrete Mathematics A. K. LalSeptember 26, 201220 CHAPTER 1. PRELIMINARIESProof. Since ∼ is reflexive, ... anti-symmetric.4. transitive.We are now ready to define a relation that appears quite frequently in mathematics. Beforedoing so, let us either use the s y mbol ∼ orR∼ for relation. That is, if ... uite a few examples of relations, let us look at some of the propertiesthat are of interest in mathematics. Definition 1.3.5. Let R be a relation on a non-empty set A. Then R is said to be1....