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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 and transitive

B

reflexive symmetric

C

symmetric and transitive

D

on equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
A
It is given that
`(x,y)inRiffx^(2)-4xy+3y^(2)=0 iff (x-3y)(x-y)=0iffx=yor x=3y`
`therefore R={(y,y):y inN}uu{(3y, y):y in N}`
Clearly, R is reflexive and transitive but not symmetric.
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