Question

Let $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3),(1,3\left)\right\}$ be a relation on the set $A=\{1,2,3\}.$ Then the relation $R$ is

[1 mark]

• A. reflexive but not symmetric
• B. reflexive but not transitive
• C. symmetric and transitive only
• D. an equivalence relation

Answer 1

The correct option is A reflexive but not symmetric

$\left(i\right)$ It is reflexive relation as all ordered pairs $(1,1),(2,2),(3,3)$ are present in $R.$

$\left(ii\right)$ $R$ is not symmetric as $(1,2)\in R$ but $(2,1)\notin R.$

$\left(iii\right)$ For transitive if $(a,b),(b,c)\in R\Rightarrow (a,c)\in R$
$(1,2),(2,3)\in R\Rightarrow (1,3)\in R$
$\therefore R$ is transitive.