# Transitive relations in a set

Having trouble understanding the concept of transitivity.
By definition: If $(a,b)\in R\wedge (b,c)\in R \Rightarrow (a,c)\in R$ - Great.

Consider the set $\{a,b\}$. What makes the relation $\{(a,a)\}$ or $\{(a,a),(a,b)\}$ transitive? How do I translate this in terms of the definition?
What makes an empty set transitive?