Let's say I have the relation $R = \{ (0,0), (1,1), (2,2), (3,3) \}$ defined on the set $X = \{ 0, 1, 2, 3 \}$.
A relation is transitive if, whenever $(a, b) \in R$ and $(b, c) \in R$, $(a, c) \in R$.
Since all of the elements of the relation are reflexive in the sense that $a = b = c$ for any sets $(a, b)$ and $(b, c)$, would we classify this relation as transitive?
I'm really just looking for confirmation as to whether it is valid to say that the relation is transitive since we have $a = b = c$ in the context of the definition of transitivity (or is it the case that $a, b, c$ must be different elements of $X$?).