In the set $A = \{1, 2, 3, 4, 5\}$, a relation $R$ is defined by $R = \{(x, y)| x, y$ $ \in A$ and $x < y\}$. Then $R$ is
Reflexive
Symmetric
Transitive
None of these
Give an example of a relation. Which is Reflexive and symmetric but not transitive.
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 the relation $R$ in $R$ defined as $R =\{(a, b): a \leq b\},$ is reflexive and transitive but not symmetric.
Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R _{1} b \Leftrightarrow a b \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$, then
If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$, then the number of relations from $A$ to $B$ is