Question

Consider the set $A=\{1,2,3\}$ and the relation on $A$ as $R=\left\{\right(1,2),(1,3\left)\right\},$ then $R$ is

• A. a reflexive relation
• B. a symmetric relation
• C. a transitive relation
• D. None of the above

Answer 1

The correct option is C a transitive relation

$R\text{is not reflexive as}(1,1),(2,2),(3,3)\text{does not belong to}R$
$R\text{is not symmetric as}(1,2)\in R\text{but}(2,1)\notin R$

$R\text{is transitive as}(1,2),(1,3)\in R\text{but there is no ordered pair starting with}2\text{or}3\text{in relation}$
i.e., the antecedent statement in transitive relation is false. So, given relation is transitive.