Let R be a reflexive and transitive relation on A. Define E in A by aEb if and only if aRb and bRa. Show that E is an equivalence relation on A. Define the relation R/E in A/E by ([a]_E)R/e([b]_E) if and only if aRb. Show that the definition does not depend on the choice of representatives for [a]_E and [b]_E. Prove that R/E is an ordering of A/E.
_ is sub.