Question:
The relation R = {(1, 2,), (1, 3)} on set A = [1, 2, 3] is _________________ only.
Solution:
Given: A relation R on the set {1, 2, 3} be defined by R = R = {(1, 2,), (1, 3)}.
R = {(1, 2,), (1, 3)}
Since, $(1,1) \notin R$
Therefore, It is not reflexive.
Since, $(1,2) \in R$ but $(2,1) \notin R$
Therefore, It is not symmetric.
But there is no counter example to disapprove transitive condition.
Therefore, it is transitive.
Hence, The relation R = {(1, 2,), (1, 3)} on set A = {1, 2, 3} is transitive only.