Let R be the realtion on the set R of all real
numbers defined by a R b if |a-b| ≤ 1. then R is
Reflexive and Symmetric
|a - a| = 0 < 1 ∴ a R a ∀ a ∈ R
∴ R is reflexive.
Again a R b ⇒ |a-b| ≤1⇒|b−a|≤1⇒bRa
∴ R is symmetric, Again 1R12 and 12RI but 12≠1
∴ R is not anti - symmetric
Further, 1R2 and 2R3 [∵|1−3|=2>1]
∴ R is not transitive.