Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is

Let $R_1$ be a relation defined by $R_1 =\{(a, b) | a \geq b, a, b \in R\}$ . Then $R_1$ is

For real numbers $x$ and $y$, we write $ xRy \in $ $x - y + \sqrt 2 $ is an irrational number. Then the relation $R$ is

Give an example of a relation. Which is Reflexive and transitive but not symmetric.

If $n(A) = m$, then total number of reflexive relations that can be defined on $A$ is-

Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l_1}$ and ${l_2}$ are said to be related by the relation $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is