Is the relation $R:=\{(1,2),(1,3)\}$ transitive on $M=\{1,2,3\}$ with $R\subseteq M\times M$?

Question

Is the relation $R:=\{(1,2),(1,3)\}$ transitive on $M=\{1,2,3\}$ with $R\subseteq M\times M$?

I think it's transitive, because we don't have elements that satisfy $xRy \land yRz $ and therefore $\forall x,y,z \in M: xRy \land yRz \implies xRz$ is always true. Is this right?

Answer 1

It is transitive, and this is vacuously true for the reason you have said.