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Which one of the following relations on R is equivalence redla

Question

Which one of the following relations on $R$ is equivalence redlation-

x R_{1} y \Leftrightarrow ∣ x ∣ = ∣ y ∣

x R_{2} y \Leftrightarrow ∣ x ∣ > ∣ y ∣

x R_{3} y \Leftrightarrow x ∣ y

x R_{4} y \Leftrightarrow x < y

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Which one of the following relations on

R

is equivalence redlation-

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Text solutionVerified

Because

∣ x ∣ = ∣ x ∣

(Reflexive)

∣ x ∣ = ∣ y ∣ \Rightarrow ∣ y ∣ = ∣ x ∣

(Symmetric)

∣ x ∣ = ∣ y ∣

and

∣ y ∣ = ∣ z ∣ \Rightarrow ∣ x ∣ = ∣ z ∣

(Transitive)

Hence option (A) is equivalence.

None of the relations given in option (b),(c)and(d) are equivalence relations because none of them are symmetric.

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Question Text	Which one of the following relations on $R$ is equivalence redlation-
Answer Type	Text solution:1
Upvotes	150