Let a relation R on the set - of natural numbers be defined as x- y - x2 -4xy-3y2-0 - x- y - Then the relation R is

Given (x, y) nbsp;⇔ x^2 –4xy+3y^2=0 nbsp; or (x, y) nbsp;⇔ (x y)(x 3y)=0 or nbsp;(x, y) nbsp;⇔ x=y or x=3y nbsp; (1) Reflexive : Clearly, (x,x) ∈ R ...

You visited us 13 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Mathematics

Reflexive Relations

Let a relatio...

Question

Let a relation $R$ on the set $N$ of natural numbers be defined as $(x, y) \Leftrightarrow x^{2} - 4 x y + 3 y^{2} = 0 \forall x, y \in N .$ Then the relation $R$ is

reflexive

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

symmetric

No worries! We‘ve got your back. Try BYJU‘S free classes today!

transitive

No worries! We‘ve got your back. Try BYJU‘S free classes today!

an equivalence relation

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A reflexive
Given $(x, y) \Leftrightarrow x^{2} - 4 x y + 3 y^{2} = 0$
or $(x, y) \Leftrightarrow (x - y) (x - 3 y) = 0$
or $(x, y) \Leftrightarrow x = y$ or $x = 3 y$

$(1)$ Reflexive :
Clearly, $(x, x) \in R$ for all $x \in N$ as $x = y$
$\Rightarrow R$ is reflexive.

$(2)$ Symmetric :
$(3, 1) \in R$ but $(1, 3) \notin R$
$\Rightarrow R$ is not symmetric.

$(2)$ Transitive :
$(9, 3), (3, 1) \in R$ but $(9, 1) \notin R$
So, $R$ is not transitive.

Suggest Corrections

Similar questions

Q. Let a relation

R

on the set

N

of natural numbers be defined as

(x, y) \Leftrightarrow x^{2} - 4 x y + 3 y^{2} = 0 \forall x, y \in N .

Then the relation

R

Q. Let a relation

R

in the set

N

of natural numbers be defined as

(x, y) \in R

if and only if

x^{2} - 4 x y + 3 y^{2} = 0

for all

x, y \in N

. The relation

R

Q. The relation

R

on the set of natural numbers

N

is defined as

x R y ⟺ x^{2} - 4 x y + 3 y^{2} = 0; x, y \in N

then

R

Q. The relation R in the set of natural number N is defined by

x R y \Leftrightarrow x^{2} - 4 x y + 3 y^{2} = 0,

x, y \in N

then R is

Q. Let

N

be the set of natural numbers and a relation

R

N

be defined by

R = {(x, y) \in N \times N : x^{3} - 3 x^{2} y - x y^{2} + 3 y^{3} = 0}

.
Then the relation

R

Join BYJU'S Learning Program

Let a relation R on the set N of natural numbers be defined as (x,y)⇔x2−4xy+3y2=0 ∀ x,y∈N. Then the relation R is

Let a relation $R$ on the set $N$ of natural numbers be defined as $(x, y) \Leftrightarrow x^{2} - 4 x y + 3 y^{2} = 0 \forall x, y \in N .$ Then the relation $R$ is