Let $R$ be the relation on the set $\mathbb{R}$ of all real numbers defined by $aRb$ if $|a-b|\le 1$. Then $R$ is:

Given relation: $aRb⟺|a-b|\le 1$.Reflexive: For any $a\in \mathbb{R}$, $|a-a|=0$. Since $0\le 1$, $aRa$ is true. $R$ is reflexive.Symmetric: If $aRb$, then $|a-b|\le 1$. We know $|a-b|=|b-a|$. So, $|b-a|\le 1$, which means $bRa$. $R$ is symmetric.Transitive: Consider $a=1,b=1.8,c=2.5$.$|a-b|=|1-1.8|=0.8\le 1⟹aRb$$|b-c|=|1.8-2.5|=0.7\le 1⟹bRc$ But $|a-c|=|1-2.5|=1.5>1⟹a/Rc$.$R$ is not transitive.Thus, $R$ is reflexive and symmetric.