Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation in $A$ given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is

The relation $R$ defined on a set $A$ is antisymmetric if $(a,\,b) \in R \Rightarrow (b,\,a) \in R$ for

Let $A=\{1,2,3\} .$ Then number of relations containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is

Show that each of the relation $R$ in the set $A =\{x \in Z : 0 \leq x \leq 12\},$ given by $R =\{(a, b):|a-b| $ is a multiple of $4\}$

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 $\}$

The relation "less than" in the set of natural numbers is