Question

Let the relation \(\rho\) be defined on \(R\) as \(a \rho b\) iff \(1+a b>0\). Then
(A) \(\rho\) is reflexive only
(B) \(\rho\) is equivalence relation
(C) \(\rho\) is reflexive and transitive but not symmetric
(D) \(\rho\) is reflexive and symmetric but not transitive

Answer 1

Ans: (D)
Hint : \(1+a^{2}>0\), so reflexive
\(1+a b=1+b a>0\) so symmetric
\(1+a b>0\) and \(1+b c>0\) does not
imply \(1+\) ac \(>0\) so not transitive

Answer 2

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Answer 3

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