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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,AAx inN`.
`therefore xRx,AAx inN`, i.e. R is reflexive.
(ii) For `x=1,y=2,2x^(2)-3xy+y^(2)=0`
`therefore 1R2`
But `2.2^(2)-3.2.1+1^(2)=3ne0`
So, 2 is not related to 1 i.e., `2cancelR1`
`therefore R` is not symmetric.
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