TITLE: Is every relation which is transitive and symmetric also reflexive?
QUESTION [9 upvotes]: I have seen a proof that every relation which is symmetric and transitive is also reflexive.
if $A=\{1,2,3\}$ Then if $R=\{(1,2)(2,1)(1,1)\color{blue}{(2,2)}\}$
here $R$ is symmetric and transitive on $A$ but not reflexive right?
Can anyone clear up this confusion for me?

REPLY [2 votes]: if you tack  $A=\{1,2,3\}$ and $R=\{(1,2),(1,1),(2,1),(2,2)\}$ then $R$ is both symetric and transitive relation on $A$ but not reflexive because $(3,3)\not\in R$