The relation R defined on the set N of natural numbers by xRy⇔2x2−3xy+y2=0 is
A
symemtric but not reflexive
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B
only symmetric
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C
not symmetric but reflexive
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D
Reflexive and symmetric
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Solution
The correct option is C not symmetric but reflexive (i) xRx⇔2x2−3xx+x2=0;∀x∈N. ∴ R is reflexive
(ii) For x=1,y=2;2x2−3xy+y2=0 ∴ 1 R 2 but 2.22−3.2.1+12=3≠0
So, 2 is not R-related to 1. ∴ R is not symmetric.