Sets and Relations Part 1

Since relation needs to be reflexive the ordered pairs (1,1),(2,2),(3,3) need to be there and (1,2) is also to be included.
Let's call R0={(1,1),(2,2),(3,3),(1,2)} the base relation.
∵A×A contain 3×3=9 ordered pairs, remaining 5 ordered are
(2,1),(1,3),(3,1),(2,3),(3,2)
We have to add at most two ordered pairs to R0 such that resulting relation is reflexive, transitive but not symmetric.
Following are the only possibilities.
R=R0U{(1,3)}
OR R0U{(3,2)}
OR R0∪{(1,3),(3,1)}
OR R0U{(1,3),(3,2)}
OR R0∪{(3,1),(3,2)}