Let $A=\{p,q,r\}.$ Which of the following is not an equivalence relation on $A ?$

$$\begin{gathered} A=\{p,q,r\} \\ {R}_1=\left\{\right(p,q),(q,r),(p,r),(p,p\left)\right\} \end{gathered}$$

$(\mathrm{q},\mathrm{q})\notin {\mathrm{R}}_1,\mathrm{so} {\mathrm{R}}_1$ is not reflexive relation.

So, $R_1$ is not an equivalence relation.

$R_2=\left\{\right(r,q),(r,p),(r,r),(q,q\left)\right\}$

Here, $(\mathrm{p},\mathrm{p})\notin {\mathrm{R}}_2,\mathrm{so} {\mathrm{R}}_2$is not reflexive relation.

So, $R_2$ is not an equivalence relation.

$R_3=\left\{\right(p,p),(q,q),(r,r),(p,q\left)\right\}$

$R_3$ is an reflexive relation.

$(p,a)\in R_3\text{ but }(q,p)\notin R_3$

$R_3$is not symmetric relation.

So, $R_3$ is not equivalence relation.