Types of Relations

Let $R$ be the relation on the set $R$ of all real numbers defined by $aRb$ if $\left|a-b\right|\le 1$. Then $R$ is

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

$R=\left\{\left(a, b\right): b \text{is divisible by} a, \text{where} a, b \in N\right\}$ is

Let $A=\left\{p,q,r,s\right\}$.

$R=\left\{\left(p,q\right),\left(q,p\right),\left(r,s\right),\left(s,r\right),\left(p,q\right)\right\}\subseteq A\times A,$Then $R$ is

The number of equivalence relations on the set $\left\{a,b,c\right\}$ is equal to

Let $R$ be the relation on the set $R$ of all real numbers defined by $aRb$ if $\left|a-b\right|\le 1$. Then $R$ is

$R\subseteq A\times A$ (where $A\ne 0)$ is an equivalence relation if $R$ is

Let $\mathrm{N}$ represent the set of natural numbers, and a relation $\mathrm{R}$ in the set $\mathrm{N}$ of natural numbers be defined as $(\mathrm{x},\mathrm{y})\iff {\mathrm{x}}^2-8\mathrm{xy}+7{\mathrm{y}}^2=0$ $\forall \mathrm{x}$. $\mathrm{R}$ is a $\_\_\_\_\_\_\_\_\_\_\_$ relation. (Choose the option that fits the blank)

On the set $A=\left\{1, 2, 3, 4\right\}$, if $R=\left\{\left(1, 3\right), \left(4, 2\right), \left(2, 4\right), \left(2, 3\right), \left(3, 1\right)\right\}$ be a relation then the relation $R$ is:

The relation $S=\left\{\left(3, 3\right),\left(4,4\right)\right\}$ on the set $A=\left\{3, 4, 5\right\}$ is ________.

Let $R=\left\{\left(3, 3\right),\left(6, 6\right),\left(9, 9\right),\left(12, 12\right),\left(6, 12\right),\left(\mathrm{3,9}\right),\left(3, 12\right),\left(3, 6\right)\right\}$ be a relation on the set $A=\left\{3,6,9,12\right\}$. The relation is

Let $A=\left\{2,4,6,8\right\}$ . A relation $R$ on $A$ is defined by $R=\left\{\left(2,4\right),\left(4,2\right),\left(4,6\right),\left(6,4\right)\right\}$ . Then $R$ is

Let $R$ and $S$ be two non-void relations on a set $A$ . Which of the following statements is false

Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm\iff n$ is a factor of $\mathrm{m}$ $($ i.e. $n|m$ $).$ Then $R$ is

With reference to a universal set, the inclusion of a subset in another, is relation, which is

Let $R$ be the relation on the set $R$ of all real numbers defined by a $R b$ iff $|a-b|\le 1$ . Then $R$ is

The number of reflexive relations of a set with four elements is equal to

$x^2=xy$ is a relation which is

Let $R=\left\{\left(3,\mathrm{ }3\right),\mathrm{ }\left(6,\mathrm{ }6\right),\mathrm{ }\left(9,\mathrm{ }9\right),\mathrm{ }\left(12,\mathrm{ }12\right),\mathrm{ }\left(6,\mathrm{ }12\right),\mathrm{ }\left(3,\mathrm{ }9\right),\left(3,\mathrm{ }12\right),\mathrm{ }\left(3,\mathrm{ }6\right)\right\}$ be a relation on the set $A=\left\{3,\mathrm{ }6,\mathrm{ }9,\mathrm{ }12\right\}$ . The relation is

Let $R$ be a relation over the set $N\times N$ and it is defined by $\left(a,b\right) R \left(c,d\right)\Rightarrow a+d=b+c.$ Then $\mathrm{ }R$ is