# Find the value

Question:

Let $A=\{1,2,3\}$ and $R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}$

Show that $R$ is reflexive but neither symmetric nor transitive.

Solution:

Given that, $A=\{1,2,3\}$ and $R=\{1,1),(2,2),(3,3),(1,2),(2,3)\}$

Now,

$\mathrm{R}$ is reflexive $\because(1,1),(2,2),(3,3) \in \mathrm{R}$

$\mathrm{R}$ is not symmetric $\because(1,2),(2,3) \in \mathrm{R}$ but $(2,1),(3,2) \notin \mathrm{R}$

$\mathrm{R}$ is not transitive $\because(1,2) \in \mathrm{R}$ and $(2,3) \in \mathrm{R} \Rightarrow(1,3) \notin \mathrm{R}$

Thus, $R$ is reflexive but neither symmetric nor transitive.