Solution to let z be the set of integers and R be the relation on Z defined … - Sikademy
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Archangel Macsika

let z be the set of integers and R be the relation on Z defined as: aRb if and only if 1+ab>0 then

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Here's the Solution to this Question

Given relation is aRb is 1+ab>0.

Considering both a and b are real numbers, we know that ab=ba


aRb=1+ab>0=>bRa=1+ba=1+ab>0

Then R is a symmetric relation.



aRa=1+a^2>0

Then R is a reflexive relation.


Let a=0.5, b=-0.5, and c=-4. Then


aRb=1+ab=1+0.5(-0.5)=0.75>0

bRc=1+bc=1+(-0.5)(-4)=3>0

But


aRc=1+ac=1+0.5(-4)=-1<0

aRc is not a relation.


Hence R is not a equivalence relation, but is a reflexive and symmetric relation.


reflexive and symmetric relation.


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