Prove that the relation R defined on the set N of natural numbers by x – InterviewSolution

InterviewSolution

1.	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.
Answer» (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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