Which one of the following relations on $R$ is an equivalence relation
$a\,{R_1}\,b \Leftrightarrow |a| = |b|$
$a{R_2}b \Leftrightarrow a \ge b$
$a{R_3}b \Leftrightarrow a \ {\rm{ divides }}\ b$
$a{R_4}b \Leftrightarrow a < b$
The relation $R$ defined on the set $A = \{1, 2, 3, 4, 5\}$ by $R = \{(x, y)$ : $|{x^2} - {y^2}| < 16\} $ is given by
If $R_{1}$ and $R_{2}$ are equivalence relations in a set $A$, show that $R_{1} \cap R_{2}$ is also an equivalence relation.
Give an example of a relation. Which is Symmetric but neither reflexive nor transitive.
Show that the number of equivalence relation in the set $\{1,2,3\} $ containing $(1,2)$ and $(2,1)$ is two.
Determine whether each of the following relations are reflexive, symmetric and transitive:
Relation $\mathrm{R}$ in the set $\mathrm{A}$ of human beings in a town at a particular time given by
$ \mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{x}$ and $ \mathrm{y}$ work at the same place $\}$