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A relation on the set of real number R is defined as follows:

Question

A relation $ρ$ on the set of real number $R$ is defined as follows:
$x ρ y$ if any only if $x y > 0$ . Then which of the following is/are true?

ρ

is reflexive and symmetric

ρ

is symmetric but not reflexive

ρ

is symmetric and transitive

ρ

is an equivalence relation

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Theodore Discussed

A relation

ρ

on the set of real number

R

is defined as follows:

x ρ y

if any only if

x y > 0

. Then which of the following is/are true?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

x ρ x : x^{2} > 0

not true for

x = 0

x ρ y \Rightarrow y ρ x

x ρ y

x y > 0, y ρ z

yz > 0

x z y^{2} > 0

, Hence

x z > 0

x ρ z

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Question Text	A relation $ρ$ on the set of real number $R$ is defined as follows: $x ρ y$ if any only if $x y > 0$ . Then which of the following is/are true?
Answer Type	Text solution:1
Upvotes	150