JEE Main 2025 — Sets and Relations Question with Solution

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