Question

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

Explanation for the correct option:

Classify the relation as symmetric, transitive, and reflexive

Given, $A=\left\{1,2,3\right\}$ and $R=\left\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\right\}$.

Since $(1,1),(2,2),(3,3)\in R,R$ is reflexive.

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

$R$ is transitive as $(1,2),(2,3)\in R$ and $(1,3)\in R.$

Hence, option $A$ is the correct answer.