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

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

Let $R$ be a reflexive relation on a finite set $A$ having $n$-elements, and let there be m ordered pairs in $R$. Then

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

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$

A relation from $P$ to $Q$ is