Q. Let $R$ be the relation on the set $R$ of all real numbers defined by $aRb$ if $|a - b| \leq 1$, then $R$ is
A) Reflexive and symmetric
B) Symmetric only
C) Transitive only
D) Anti-symmetric only
Explanation
(a)
$aRa$ if $|a - a| = 0 < 1$, which is true.
$\therefore$ It is reflexive.
Now, $aRb$,
$|a - b| \leq 1 \Rightarrow |b - a| \leq 1$
$\Rightarrow \ \ \ aRb \Rightarrow bRa$
$\therefore$ It is symmetric.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.