Question:
Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is
(a) neither reflexive nor transitive
(b) neither symmetric nor transitive
(c) transitive
(d) none of these
Solution:
(c) transitive
Reflexivity : Since $(1,1) \notin B, B$ is not reflexive on $A$.
Symmetry : Since $(1,2) \in B$ but $(2,1) \notin B, B$ is not symmetric on $A$.
Transitivity : Since $(1,2) \in B,(2,3) \in B$ and $(1,3) \in B, B$ is transitive on $A$.