Question:
If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is
(a) symmetric and transitive only
(b) reflexive and transitive only
(c) symmetric only
(d) transitive only
Solution:
(a) symmetric and transitive only
Reflexivity: Since $(b, b) \notin R, R$ is not reflexive on $A$.
Symmetry : Since $(a, b) \in R$ and $(b, a) \in R, R$ is symmetric on $A$.
Transitivity : Since $(a, b) \in R, \quad(b, a) \in R$ and $(a, a) \in R, R$ is transitive on $A$.