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If a relation R on the set N of natural ...

If a relation `R` on the set `N` of natural numbers is defined as `(x,y)hArrx^(2)-4xy+3y^(2)=0,Aax,yepsilonN`. Then the relation `R` is

A

reflexive

B

symmetric

C

transitive

D

an aquivalence relation

Text Solution

Verified by Experts

The correct Answer is:
A
Given
`(x,y)hArrx^(2)-4xy+3y^(2)=0`
or `(x,y)hArr(x-y)(x-3y)=0`
Reflexive `xRx` as
`(x-x)(x-3x)=0`
Thus, it is reflexive.
Symmetric
Now, let `xRy`, then `(x-y)(x-3)=0`
by `yRx` as `(y-x)(y-3x)!=0`
So, it is not symmetric.
Similarly, it is not transitive.
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