Relation on $\mathbb{N}$ that is only transitive

Question

Can a relation on $\mathbb{N}$ be only transitive, not reflexive nor symmetric nor antisymmetric?

I started with the usual $<$ that only satisfies transitivity but also antisymmetry. Then I tried adding some pair $(a,b)$ to my relation, violating antisymmetry. But in every try either reflexity or symmetry were satisfied then…

Answer 1

An example is the relation $\{1,2\}^2\cup\{(3,4)\}.$