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Prove that the relation R defined on the...

Prove that the relation R defined on the set N of natural numbers by xRy `iff 2x^(2) - 3xy + y^(2) = 0` is not symmetric but it is reflexive.

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(i) `2x^(2) - 3x.x + x^(2) = 0, AA xx in N`.
`:.` xRx `AA xx in N` i.e., R is reflexive.
(ii) For x = 1, y = 2, `2x^(2) - 3xy + y^(2) = 0`. So (1, 2) `in R`
But `2.2^(2) - 3.2.1 + 1^(2) = 3 != 0`. So 2 is not R - related to 1. i.e., R is not Symmetric.
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