Which one of the following relations on $R$ is an equivalence relation
$a\,{R_1}\,b \Leftrightarrow |a| = |b|$
$a{R_2}b \Leftrightarrow a \ge b$
$a{R_3}b \Leftrightarrow a \ {\rm{ divides }}\ b$
$a{R_4}b \Leftrightarrow a < b$
Let $R$ and $S$ be two equivalence relations on a set $A$. Then
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.
Determine whether each of the following relations are reflexive, symmetric and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time given by
$R =\{(x, y): x$ and $y$ live in the same locality $\}$
Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = {1, 2, 3}$, the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is
Show that the relation $R$ in the set $R$ of real numbers, defined as $R =\left\{(a, b): a \leq b^{2}\right\}$ is neither reflexive nor symmetric nor transitive.