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

Let $S$ be set of all real numbers ; then on set $S$ relation $R$ defined as $R = \{\ (a, b) : 1 + ab > 0\ \}$ is

Let $R$ and $S$ be two equivalence relations on a set $A$. Then

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

Relation $\mathrm{R}$ in the set $\mathrm{Z}$ of all integers defined as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{x}-\mathrm{y}$ is an integer $\}$

If $A = \{1, 2, 3\}$ , $B = \{1, 4, 6, 9\}$ and $R$ is a relation from $A$ to $B$ defined by ‘$x$ is greater than $y$’. The range of $R$ is

Among the relations $S =\left\{( a , b ): a , b \in R -\{0\}, 2+\frac{ a }{ b } > 0\right\}$ And $T =\left\{( a , b ): a , b \in R , a ^2- b ^2 \in Z \right\}$,