Let R be a relation on R, given by R={(a, b): | vedclass

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Question

Check for reflexivity:

As $3(a-a)+\sqrt{7}=\sqrt{7}$ which belongs to relation so relation is reflexive

Check for symmetric:

Take $a=\frac{\s

Vedclass · Accepted Answer

Reflexive but neither symmetric nor transitive

Vedclass · Answer

Check for reflexivity:

As $3(a-a)+\sqrt{7}=\sqrt{7}$ which belongs to relation so relation is reflexive

Check for symmetric:

Take $a=\frac{\sqrt{7}}{3}, b=0$

Now $(a, b) \in R$ but $(b, a) 
otin R$

As $3(b-a)+\sqrt{7}=0$ which is rational so relation is not symmetric.

Check for Transitivity:

Take $(a, b)$ as $\left(\frac{\sqrt{7}}{3}, 1ight)$

$\&(b, c)$ as $\left(1, \frac{2 \sqrt{7}}{3}ight)$

So now $( a , b ) \in R \&( b , c ) \in R$ but $( a , c ) 
otin R$ which means relation is not transitive

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

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