Question

Let $S$ be the set of all real numbers. Then the relation $R=\left\{\right(a,b):1+ab>0\}$ on S is

• A. Reflexive and symmetric but not transitive
• B. Reflexive and transitive but not symmetric
• C. Symmetric and transitive but not reflexive
• D. Equivalence relation

Answer 1

The correct option is A Reflexive and symmetric but not transitive

$R=\left\{\right(a,b):1+ab>0\}$
$\because (a,b)\in R$
$\therefore (b,a)\in R$ because $1+ab>0$
So it is symmetric
also $(a,a)\in R$, $1+a^2>0$
so it is Reflexive. It is not transitive.