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

<b>For reflexive :</b> <br/><br/>$3 a-3 a+\sqrt{7}$ is an irrational number $\forall a \in R R$ is reflexive <br/><br/><b>For symmetric :</b> <br/><br/>Let $3 a-3 b+\sqrt{7}$ is an irrational number <br/><br/>$\Rightarrow 3 b-3 a+\sqrt{7}$ is an irrational number <br/><br/>For example, Let $3 a-3 b=\sqrt{7}$ <br/><br/>$\sqrt{7}+\sqrt{7}$ is irrational but $-\sqrt{7}+\sqrt{7}$ is not. <br/><br/>$\therefore R$ is not symmetric <br/><br/><b>For transitive :</b> <br/><br/>Let $3 a-3 b+\sqrt{7}$ is irrational and $3 b-3 c+\sqrt{7}$ is irrational. <br/><br/>$\Rightarrow 3 a-3 c+\sqrt{7}$ is irrational. <br/><br/>For example, take $a=0, b=-\sqrt{7}, c=\frac{\sqrt{7}}{3}$ <br/><br/>$R$ is not transitive.