Q. Let $S$ be the set of all real numbers. Then, the relation $R = \{(a,\ b):1 + ab > 0\}$ 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) Reflexive, transitive and symmetric
Explanation
(a)
$R = \{(a,\ b):1 + ab > 0\}$
It is clear that the given relation on $S$ is reflexive, symmetric but not transitive.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.