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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