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Question

The following relation is defined on the set of real numbers:
aRb, if ab>0
Find whether the relation is reflexive, symmetric or transitive.

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Solution

Given the relation is defined on the set of real numbers:
aRb if ab>0.
Now this relation is not reflexive as aR/a, since aa=00 aR.
Similarly the relation is not symmetric as aRbbRa since ab>0 this gives ba<0 a,bR.
But the relation is transitive as aRb and bRcaRc since ab>0 and bc>0 simply gives (ab)+(bc)>0 or ac>0 a,b,cR.

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