Question:
State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive.
Solution:
Since $(1,2) \in R,(2,1) \in R$ but $(1,1) \notin R, R$ is not transitive on the set $\{1,2,3\}$.
For $R$ to be in a transitive relation, we must have $(1,1) \in R$.