Question

The relation R defined on the set N of natural numbers by $xRy\iff 2x^2-3xy+y^2=0$ is

• A. symemtric but not reflexive
• B. only symmetric
• C. not symmetric but reflexive
• D. Reflexive and symmetric

Answer 1

The correct option is C not symmetric but reflexive

(i) $xRx\iff 2x^2-3xx+x^2=0;\forall x\in N$.
$\therefore$ R is reflexive
(ii) For $x=1,y=2;2x^2-3xy+y^2=0$
$\therefore$ 1 R 2 but ${2.2}^2-\mathrm{3.2.1}+1^2=3\ne 0$
So, 2 is not R-related to 1.
$\therefore$ R is not symmetric.