Can a relation with less than 3 elements be considered transitive? The generalize rule for a transitive relation is 
a -> b
b -> c
therefor
a -> c

If an element has less than 3 elements, can it still be transitive? If so, does that provide any useful information?

Yes, and yes, respectively. For example, the relation $\{(a,b),(b,a)\}$ is not transitive; its transitive closure is $\{(a,a),(a,b),(b,a),(b,b)\}$. So the useful information you get from knowing that you have a transitive relation containing $(a,b)$ and $(b,a)$ is that you must also have $(a,a)$ and $(b,b)$.
