Test whether, `R_3` on `R` defined by `(a ,\ b) in R_3<=> a^2-4\ a b+3b^2=0` .

Explanation

(iii) Given as `R_{3}` on `R` defined by

`(a, b) \in R_{3} \Leftrightarrow a^{2}-4 a b+3 b^{2}=0`

Now let us check whether `R_{2}` is reflexive, symmetric and transitive.

Reflexivity:

Let a be an arbitrary element of `R_{3}`.

Then, `a \in R_{3} \Rightarrow a^{2}-4 a \times a+3 a^{2}=0`

Clearly, `R_{3}` is reflexive Symmetry:

Let `(a, b) \in R_{3} \Rightarrow a^{2}-4 a b+3 b^{2}=0`

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