Is this relation transitive?

Question

R: { (1,1), (1,3), (2,2), (3,1) }

My answer is no. My logic is that If (3,1) is in the relation, and (1,3) is in the relation, that implies that (3,3) must also be in the relation.

Just wanted to verify if this is correct.

Answer 1

Yes, this is correct. In fact, $R'=\{(1,1),(1,3),(2,2),(3,1),(3,3)\}$ is a relation, so this is the only counterexample.