Problem 10.2 (d,e, g). WARNING: DG use the notation to denote an arbitrary relation, not just an equivalence relation. I think it better to use Rfor a general relation, and just for equivalence relations.

10 Relations 107 Problem 10.2. Decide whether or not the following relations are reflexive, sym- metric, or transitive. If a property holds, prove that it does. If a property does not hold, prove that it does not hold. If the relation is an equivalence relation, give the equivalence class of a general point x E X. (a) On R, we define x ~ y if and only if x