Let R be the relation on the set R of all real numbers defined by a R b if a-b≤1. Then R is

a-a=0<1 ∴aRa∀a∈R∴R is reflexive.Again aRb⇒a-b≤1⇒b-a≤1⇒bRa∴ R is symmetric, Again 1R12 and 12R1 but 12≠1∴R is not anti-symmetric.Further, 1 R 2 and 2 R 3 but 1ℝ3, [∵ 1-3=2>1]∴R is not transitive.