# The relation R

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 = {(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.