We have a relation R = {$(a,a),(b,b)$}.
Is this relation transitive? If that is true, then why is it transitive? According to definition a relation is transitive
If (a,b) in R & (b,c) in R then (a,c) in R
$\forall a,b,c \in R: a R b \land b R c \implies a R c$.
But in our set we're missing the element c so how could it be transitive?
On
It is definitely a TRANSITIVE RELATION. see for transitive we say IF ( IF word is important ) if (a,b) belongs to a set , and (b,c) belongs to set ,then ( a,c) must be there for the set to be transitive. OR if these type of order pair are absent( like in your question) it is definitely transitive
The relation will not be transitive only if there is a counterexample - where $(x,y)$ and $(y,z)$ are related but $(x,z)$ are not.
There we have no such counterexample example.
Note: Don't confuse $a,b,c$ being used as variables in a definition, with $\rm a,b,c$ being used as enumerator values in the sets.