If $R \subset A \times B$ and $S \subset B \times C\,$ be two relations, then ${(SoR)^{ - 1}} = $

An integer $m$ is said to be related to another integer $n$ if $m$ is a multiple of $n$. Then the relation is

Consider set $A = \{1,2,3\}$ . Number of symmetric relations that can be defined on $A$ containing the ordered pair $(1,2)$ & $(2,1)$ is

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $\mathrm{R}$ in the set $\mathrm{N}$ of natural numbers defined as

$\mathrm{R}=\{(x, y): y=x+5 $ and $ x<4\}$

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............

Let $A = \{p, q, r\}$. Which of the following is an equivalence relation on $A$