Question

Let a relation R on the set N of natural numbers be defined as (x, y)  R if and only if x2 – 4xy + 3y2
= 0
for all x, y  N. The relation R is

options -
(A*) Reflexive (B) Symmetric (C) Transitive (D) Equivalence Relation
I want explanation please

Answer 1

We have R={(x,y):x2−4xy+3y2=0,x,y∈N}.

Let x∈N.x2−4xx+3x2=4x2−4x2=0

∴(x,x)∈R.

∴R is reflexive

We have (3)2−4(3)(1)+3(1)2=9−12+3=0

∴(3,1)∈R.

Also (1)2−4(1)(3)+3(3)2=1−12+27=16=0

∴(1,3)∈/R.

∴R is not symmetric.

(9,3)∈R because

(9)2−4(9)(3)+3(3)2=81−108+27=0

Also (3,1)∈R because

(3)2−4(3)(1)+3(1)2=9−12+3=0

Now, (9,1

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