The void relation on a set $A$ is
Reflexive
Symmetric and transitive
Reflexive and symmetric
Reflexive and transitive
If $A = \left\{ {x \in {z^ + }\,:x < 10} \right.$& and $x$ is a multiple of $3$ or $4\}$, where $z^+$ is the set of positive integers, then the total number of symmetric relations on $A$ 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 $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ is
Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,2),(2,1)\}$ is symmetric but neither reflexive nor transitive.
Determine whether each of the following relations are reflexive, symmetric and transitive:
Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,4,5,6\}$ as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{y}$ is divisible by $\mathrm{x}\}$