The relation $R$ is define over set $S=\left \{0,1,2,3 \right\}$ is as follows:
$R=\left\{ (0,0) (1,1) (2,2) (3,3 ) (0,1) (1,0) (1,2) (2,1) (2,3) (3,2)\right\}$
- $R$ is reflexive relation as all digonal elements is present; selfloop at each node.
- $R$ is symmetric relation as bidirectional edges present between every node; $(0,1)\in R\rightarrow (1,0)\in R$. we can check other possibility also.
- $R$ is not antisymmetric as $(0,1) ,(1,0)$ both pairs is present in the relation.
- $R$ is not transitive relation because $(0,1)\in R,(1,2)\in R\rightarrow(0,2)\notin R$