Types of Relations

Let $A=\{4,5,6\}$ and relation $R$ on set $A$ as $R=\left\{\left(x,y\right);|x-y|=10\right\}$.Check whether the relation $R$ is an empty relation or not. Explain your answer.

Let $A=\{1,2,3,4\}$ and relation $R$ on set $A$ as $R=\left\{\left(x,y\right);|x-y|=7\right\}$.Check whether the relation $R$ is an empty relation or not. Explain your answer.

Let $A=\{1,2,3\}$ and relation $R$ on set $A$ as $R=\left\{\left(x,y\right);|x-y|=8\right\}$.Check whether the relation $R$ is an empty relation or not. Explain your answer.

Let $A=$ Set of all students in a girls school and we define relation $R$ on set $A$ as $R=\left\{\right(a,b):a\text{ and }b\text{ are brothers }\}$.Check whether the relation $R$ is an empty relation or not. Explain your answer.

A relation $R$ on set $A=\{4,5,6\}$ is defined by $R=\left\{\right(x,y)\in R:|x-y|\ge 0\}$. Check whether the relation $R$ is universal relation or not. Explain your answer.$$

A relation $R$ on set $A=\{1,2,3,4,5,6\}$ is defined by $R=\left\{\right(a,b)\in R:|a-b|\ge 0\}$. Check whether the relation $R$ is universal relation or not. Explain your answer.$$

Let $A=$Set of all students in a girls school and we define relation $R$ on set $A$ as $R=\left\{\right(a,b):\text{ height of }a\&b\text{ is greater than }10 \text{cm}\}$. Check whether the relation $R$ is universal relation or not. Explain.

If $\left|A\right|=5 \& \left|B\right|=4$ then the number of elements in the largest relation that can be defined from $A$ into $B$ is.

Let $S$ be the set of all straight lines in a plane. Let $R$ be a relation on $S$ defined by $a R b \iff a\perp b$. Then, $R$ is

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

Let Z denote the set of all integers. If a relation R is defined on Z as follows:
( x, y) $\in$ R if and only if x is multiple of y, then 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 $R$ be a relation on the set $N$ be defined by $\mathrm{ }\left\{\left(x, y\right)| x, y\in N, 2x + y = 41\right\}$ . 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