(Relation between two sets) If $X$ and $Y$ are sets, a relation between $X$ and $Y$ is a subset $R \subset X \times Y.$ For a relation $R \subset X\times Y$ and $a \in X$ and $b \in Y$ if $(x,y) \in R,$ we write $xRy$ and if $(x,y)\notin R,$ we write $x/R/y.$ (let /R/ be a slash across the R similar to what I have with $\notin$.)
My question:
Prove that $X \times Y$ is an equivalence relation. We have that there is a relation $R$ on $X$ and another relation $R'$ on $Y$ and that both are equivalence relations. The goal is to prove that $R \times R'$ is an equivalence relation.
My thoughts: I am trying to teach this to myself. Some friend of mine was talking about this and I did not know too much about these types of question. I decided to learn this by myself and saw this question.
How would we do this? Can someone please help me with this? I would like to see how this proof is done.
This is what Hugh Denoncourt was saying in his comment.