For the basic case Let $X=Y= \mathbb{R}$ and $R(X,Y)= \{(x,y) \in X \times Y : y=x^{2} \}$.
I know it's not symmetric, not reflexive, not transitive. How do I provide a counterexample that it's not an equivalence relation? I'm not entirely sure how to format this in the best way. Would providing a counter example be better ?