On the set R of real numbers we define xP y if and only if xy - 0- Then the relation P isA- reflexive but not symmetricB- symmetric but not reflexiveC- transitive but not reflexiveD- reflexive and symmetric but not transitive

The correct option is D reflexive and symmetric but not transitivex · x = x^2 ≥ 0, ∀ x ∈ℝ ∴ P is reflexive. Let x,y ∈ nbsp;ℝ such that xy≥0 ⇒ yx ≥ 0, ∀ x,y ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Reflexive Relations

On the set R ...

Question

On the set $R$ of real numbers we define $x P y$ if and only if $x y \geq 0$ . Then the relation $P$ is

reflexive but not symmetric

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

symmetric but not reflexive

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

transitive but not reflexive

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

reflexive and symmetric but not transitive

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

Open in App

Solution

The correct option is D reflexive and symmetric but not transitive
$x \cdot x = x^{2} \geq 0, \forall x \in R$
$∴ P$ is reflexive.

Let $x, y \in R$ such that $x y \geq 0$
$\Rightarrow y x \geq 0, \forall x, y \in R$
$\Rightarrow y P x$
$\Rightarrow P$ is symmetric.

$(1, 0), (0, - 2) \in P$ but $(1, - 2) \notin P$
$∴$ the relation $P$ is not transitive.

Suggest Corrections

Similar questions

Q. On

R

, the relation

ρ

be defined by '

x ρ y

holds if and only if

x - y

is zero or irrational". Then

Q. For any two real number

θ

and

ϕ

where,

θ, ϕ \in (\frac{- π}{2}, \frac{π}{2}) .

We define

θ R ϕ

if and only if

{sec}^{2} θ - {tan}^{2} ϕ = 1.

Then relation

R

Q. Let R be a relation defined by

R = {(a, b) | a \geq b; a, b ϵ R}

, then R is

Q. The relation

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}

on the set

A = {1, 2, 3}

Q. Mark the correct alternative in the following question:

The relation S defined on the set R of all real number by the rule aSb iff a

\geq

b is

(a) an equivalence relation
(b) reflexive, transitive but not symmetric
(c) symmetric, transitive but not reflexive
(d) neither transitive nor reflexive but symmetric

Join BYJU'S Learning Program

On the set R of real numbers we define xPy if and only if xy≥0. Then the relation P is

The correct option is D reflexive and symmetric but not transitivex⋅x=x2≥0, ∀ x∈R ∴P is reflexive. Let x,y∈R such that xy≥0 ⇒yx≥0, ∀ x,y∈R ⇒yPx ⇒P is symmetric. (1,0),(0,−2)∈P but (1,−2)∉P ∴ the relation P is not transitive.

On the set $R$ of real numbers we define $x P y$ if and only if $x y \geq 0$ . Then the relation $P$ is