Let N be the set of natural numbers and a relation R on N be...

${x}^{3} - 3{x}^{2}y - x{y}^{2} + 3{y}^{3} = 0$

$⇒ x\left({x}^{2} - {y}^{2}\right) - 3y\left({x}^{2} - {y}^{2}\right) = 0$

$⇒ \left(x - 3y\right)\left(x - y\right)\left(x + y\right) = 0$

Now, $x = y \forall \left(x, y\right) \in N \times N$ so its a reflexive relation.
But not symmetric & transitive

Since, $\left(3, 1\right)$ satisfies but $\left(1, 3\right)$ does not.

Also \left(3, 1\right) \text{and }\left(1, - 1\right) satisfies but \left(3, - 1\right) does not.</p>