Why is the Relation R3 Transitive?

Question

Given $A = \{1,2,3,4\}$

in the Relation $\mathcal{R} = \{(1,1),(2,2),(3,3),(4,4)\}$

I understand why $\mathcal{R}$ is Reflexive, Symmetric

but why is it also transitive?

In my understanding for a relation to be transitive for this particular example it must have something like $(1, 2), (2,3), (1,3)$ to be transitive.

Answer 1

It is transitive, but in a trivial way. One way to think about this is that there is no triplet that contradicts transitivity! Then by the excluded middle property ($P\land\neg P=True$) the relation is transitive.

You can also reason like this: Let $aRb$ and $bRc$. The. $a=b=c$, because of the properties of the relation. Then $aRc$.