Question

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

• A. Reflexive but not symmetric
• B. Reflexive but not transitive
• C. Symmetric and transitive
• D. Neither symmetric nor transitive

Answer 1

The correct option is A Reflexive but not symmetric

$(1,1),(2,2),(3,3)\in R$
$\Rightarrow R$ is reflexive
$(1,2)\in R$ but $(2,1)\notin R$
$\Rightarrow R$ is not symmetric
$(1,2)\in R,(2,3)\in R,(1,3)\in R$
$\Rightarrow R$ is transitive.