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Question

Let R be the relation on the set R of all real numbers defined by aRb iff |ab|1. Then R is


A

Reflexive and symmetric

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B

Symmetric only

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C

Transitive only

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D

Antisymmetric only

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Solution

The correct option is A

Reflexive and symmetric


Explanation For The Correct Option:

Determining the correct option

The given relation

aRb iff |ab|1

Checking Reflexivity

aRa|aa|=0<1

So, R is reflexive.

Checking Symmetricity

aRb|ab|1|ba|1bRa

So, R is symmetric.

Checking transitivity

If 1R21-2=11

And 2R33-2=11

Now for 1R31-3=21

So 1R3

Thus R in not transitive

Checking Anti symmetricity

If 1R21-2=11

And 2R33-2=11

But 12

Thus R us not anti symmetric

R is not transitive.

Hence, option A is the correct answer.


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