Let $R$ be the relation on the set $R$ of all real numbers defined by $a \ R \ b$ if $|a - b| \le 1$. Then $R$ is

Let $S=\{1,2,3, \ldots, 10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R=\{(A, B): A \cap B \neq \phi ; A, B \in M\}$ is :

Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A \times B$ such that $R =$ $\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right): a_1 \leq b_2\right.$ and $\left.b_1 \leq a_2\right\}$. Then the number of elements in the set $R$ is

Show that the relation $\mathrm{R}$ in the set $\mathrm{Z}$ of integers given by $\mathrm{R} =\{(\mathrm{a}, \mathrm{b}): 2$ divides $\mathrm{a}-\mathrm{b}\}$ is an equivalence relation.

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

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x $ is father of $y\}$

Let $A = \{ 2,\,4,\,6,\,8\} $. $A$ relation $R$ on $A$ is defined by $R = \{ (2,\,4),\,(4,\,2),\,(4,\,6),\,(6,\,4)\} $. Then $R$ is