Let a relation $R$ on $\mathbb{N} \times \mathbb{N}$ be defined as : $\left(\mathrm{x}_1, \mathrm{y}_1\right) \mathrm{R}\left(\mathrm{x}_2, \mathrm{y}_2\right)$ if and only if $\mathrm{x}_1 \leq \mathrm{x}_2$ or $\mathrm{y}_1 \leq \mathrm{y}_2$

Consider the two statements :

($I$) $\mathrm{R}$ is reflexive but not symmetric.

($II$) $\mathrm{R}$ is transitive

Then which one of the following is true?

The relation $R$ defined in $N$ as $aRb \Leftrightarrow b$ is divisible by $a$ is

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $\mathrm{R}$ in the set $\mathrm{N}$ of natural numbers defined as

$\mathrm{R}=\{(x, y): y=x+5 $ and $ x<4\}$

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 

Let $r$ be a relation from $R$ (Set of real number) to $R$ defined by $r$ = $\left\{ {\left( {x,y} \right)\,|\,x,\,y\, \in \,R} \right.$ and $xy$ is an irrational number $\}$ , then relation $r$ is