$\text{ The relation }R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3),(1,3\left)\right\}\text{ on set }A=\{1,2,3\}\text{ is }$

$\text{ As }(1,1);(2,2);(3,3)\in R,R\text{ is reflexive }$
$\text{ As }(1,2)\in R\text{ but }(2,1)\notin R,R\text{ is not symmetric }$

It can be easily seen that R is transitive