Let $R$ be a relation on $Z \times Z$ defined by$ (a, b)$$R(c, d)$ if and only if $ad - bc$ is divisible by $5$ . Then $\mathrm{R}$ is

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 $\}$

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

The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is

Let $A = \{1, 2, 3\}, B = \{1, 3, 5\}$. $A$ relation $R:A \to B$ is defined by $R = \{(1, 3), (1, 5), (2, 1)\}$. Then ${R^{ - 1}}$ is defined by

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