Let $R$ be a reflexive relation on a finite set $A$ having $n$-elements, and let there be m ordered pairs in $R$. Then
$m \ge n$
$m \le n$
$m = n$
None of these
Let $I$ be the set of positve integers. $R$ is a relation on the set $I$ given by $R =\left\{ {\left( {a,b} \right) \in I \times I\,|\,\,{{\log }_2}\left( {\frac{a}{b}} \right)} \right.$ is a non-negative integer$\}$, then $R$ is
If $R \subset A \times B$ and $S \subset B \times C\,$ be two relations, then ${(SoR)^{ - 1}} = $
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
Show that the relation $R$ in the set $A$ of all the books in a library of a college, given by $R =\{(x, y): x $ and $y$ have same number of pages $\}$ is an equivalence relation.
Let $N$ denote the set of all natural numbers and $R$ be the relation on $N \times N$ defined by $(a, b)$ $R$ $(c, d)$ if $ad(b + c) = bc(a + d),$ then $R$ is