1. The problem statement, all variables and given/known data Let R be a reflexive and transitive relation on a set A. Define another relation, S, such that, for any x, y ∈ A, Sxy iff (Rxy and Ryx). Prove: S is an equivalence relation on A. 2. Relevant equations S is an equivalence relation if it is symmetric, reflexive and transitive. S is reflexive if for every x, then Rxx. S is symmetric if for every x,y - if Rxy, then Ryx. S is transitive if for every x,y,z - if (Rxy and Ryx) then x = y. 3. The attempt at a solution What I do not understand is how to get any information about S other than Sxy. For example if I need to prove that S is symmetric, then I need Sxx. How can I know Sxx when the only info I have about the relation S is about Sxy? I would really appreciate some help on this problem - I have been stuck for days!