(adsbygoogle = window.adsbygoogle || []).push({}); 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Please help me solve a set relation problem!

**Physics Forums | Science Articles, Homework Help, Discussion**