$R$ is a relation over the set of real numbers and it is given by $nm \ge 0$. Then $R$ is

Check whether the relation $R$ defined in the set $\{1,2,3,4,5,6\}$ as $R =\{(a, b): b=a+1\}$ is reflexive, symmetric or transitive.

Let $A = \{1, 2, 3, 4\}$ and let $R= \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then $R$ is

Let $n$ be a fixed positive integer. Define a relation $R$ on the set $Z$ of integers by, $aRb \Leftrightarrow n|a – b$|. Then $R$ is

Let $R$ be a relation on the set $A$ of ordered pairs of positive integers defined by $(x, y) R (u, v)$ if and only if $x v=y u .$ Show that $R$ is an equivalence relation.