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
Reflexive and symmetric but not transitive
Reflexive but neither symmetric not transitive
Reflexive, symmetric and transitive.
Reflexive and transitive but not symmetric
Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$. Then $R$ is
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 exactly $7\,cm $ taller than $y\}$
Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,1),\,(2,2),$ $(3,3)$, $(1,2)$, $(2,3)\}$ is reflexive but neither symmetric nor transitive.
If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is
Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is