Mathematics - Sets and Relations Question with Solution | TestHub

$R$ is reflexive $\Rightarrow R$ have $(1,1),(2,2),(3,3)$ $R$ is transitive $\begin{array}{rl}& \because (1,2),(23)\in R\therefore (1,3)\in R\\ & \therefore R_1=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\end{array}$ Clearly $R_1$ is reflexive and transitive but not symmetric. Similarly, $\begin{array}{rl}& R_2=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,2)\}\\ & R_3=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(2,1)\}\end{array}$ Therefore, 3 relations are possible