Question

Let $R=\left\{\right(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6\left)\right\}$ be a relation on the set $A=\{3,6,9,12\}.$ Then the relation is

• A. Reflexive and transitive only
• B. Reflexive only
• C. Reflexive, symmetric and transitive
• D. Reflexive but neither symmetric nor transitive

Answer 1

The correct option is A Reflexive and transitive only

$\left(i\right)$ It is reflexive relation as all ordered pairs $(3,3),(6,6),(9,9),(12,12)$ are present in $R$
$\left(ii\right)R$is not symmetric as $(6,12)\in R$ but $(12,6)\notin R$
$\left(iii\right)$ For transitive if $(a,b),(b,c)\in R\Rightarrow (a,c)\in R$
i.e., $(3,6),(6,12)\in R\Rightarrow (3,12)\in R$

As the given relation $R$ satisfies the above condition.
Hence, $R$ is transitive.