Question

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

• A. reflexive
• B. transitive
• C. symmetric
• D. none of these

Answer 1

Answer: (C)

$R$ is not reflexive as $\left(\right.2,2\left.\right)\notin R,\left(\right.3,3\left.\right)\notin R$
Also, $R$ is not transitive as $\left(\right.2,1\left.\right)$ $\in R$ and $\left(\right.1,2\left.\right)$ $\in R$ but $\left(\right.2,2\left.\right)\notin R$ .
However $R$ is symmetric.