Let $R$ be a relation on $\mathrm{ℝ}$, given by 
$R=\left\{(a,b):3a-3b+\sqrt{ 7} is an irrational number\right\}$
Then $R$ is

Reflexive 3a - 3a + $\sqrt{7}$ = $\sqrt{7}$ is irrational
(a, a) $\in$ R
Not symmetric if (a, b) $\in$ R but (b, a) $\notin$ R
$\mathrm{if} \mathrm{a}=\frac{\sqrt{7}}{3},\mathrm{b}=7 then ,it is not symmetric$

$$\begin{gathered} \text{ Take }(a,b)\text{ as }\left(\frac{\sqrt{7}}{3},1\right) \\ \mathrm{\&}(\mathrm{b},\mathrm{c})\text{ as }\left(1,\frac{2\sqrt{7}}{3}\right) \\ \text{ So now }(\mathrm{a},\mathrm{b})\in \mathrm{R}\mathrm{\&}(\mathrm{b},\mathrm{c})\in \mathrm{R}\text{ but }(\mathrm{a},\mathrm{c})\notin \mathrm{R} \\ \text{ which means relation is not transitive } \end{gathered}$$