I was solving this question:
On a set S , $a\;R\;b$ if $a=b$ , prove it's an equivalence relation
Edited proof:
$R = \{(x,x) \;|\; x \in S \} $
since every element $x=x$ under the relation $R$ for all $x \in S$ , hence it's reflexive
$ \forall\; (x,y) \in R$ , since $x=y$ then $y=x$ also, hence it's symmetric
$ \forall\; (x,y),(y,z) \in R$ since $x=y$ and $y=z$ $=>$ $x=z$, hence it's transitive
I want to ask whether my proof is right? And if right did I do mathematically or more in layman's term?
Thanks
Edit: Now it seems R contains only one element $(a,a)$