Let R1 and R2 be two relations defined on R by a R1 b Û ab ≥ 0 and a R2 b ⇔ a ≥ b Then,

For R1, take a = 1, b = 0, c = -1 a b ≥ 0 , b c ≥ 0 but AC < 0 So R1 is not an equivalence relation. For R2, it will not be symmetric. So R2 is also not an equivalence relation.

Let R₁ and R₂ be two relations defined on R by

a R₁b Û ab $\geq 0$ and a R₂ b $\Leftrightarrow a \geq b$

Then,

Option 1 - R1 is an equivalence relation but not R2

Option 2 - R2 is an equivalence relation but not R1

Option 3 - Both R1 and R2 are equivalence relations

Option 4 - Neither R1 nor R2 is an equivalence relation

3 Views|Posted 8 months ago

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Answered by

Alok Kumar Singh | Contributor-Level 10

8 months ago

Correct Option - 4

Detailed Solution:

For R₁, take a = 1, b = 0, c = -1

$a b \geq 0, b c \geq 0$ but AC < 0

So R₁ is not an equivalence relation.

For R₂, it will not be symmetric.

So R₂ is also not an equivalence relation.

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