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Question

The relation R defined on the set N of natural numbers by xRy2x23xy+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) xRx2x23xx+x2=0; x N.
R is reflexive
(ii) For x=1,y=2;2x23xy+y2=0
1 R 2 but 2.223.2.1+12=30
So, 2 is not R-related to 1.
R is not symmetric.

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