Question:
If a relation R on the set (1, 2, 3) be defined by R = {(1, 2)}, then R is
(a) reflexive (b) transitive (c) symmetric (d) none of these
Solution:
Given: A relation R on the set {1, 2, 3} be defined by R = {(1, 2)}.
R = {(1, 2)}
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 correct option is (b).
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