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Let R = {(x, y) : x, y in N and x^2-4xy...

Let `R = {(x, y) : x, y in N and x^2-4xy+3y^2 = 0}`, where `N` is the set of all natural numbers. Then the relation R is

A

reflexive

B

symmetric

C

transitive

D

an equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `(x,y)iffx^(2)-4xy+3y^(2)=0`
or `" "(x,y)iff(x-y)(x-3y)=0`
Reflexive `xRRx" as"(x-x)(x-3x)=0`
Thus, it is reflexive.
Symmetric
Now, let `xRRy," then"(x-y)(x-3y)=0`
but `" ""yRx as"(y-x)(y-3x)ne0`
So, it is not symmetric.
Similarly, it is not transitive.
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