Types of Relations

The relation $R$can be defined in the set$\left\{1,2,3,4,5,6\right\}$ as  $R=\left\{(a,b):b=a+1\right\}$ .It is an example of 

Relation $R$ in the set $A=\left\{1,2,3,4,5,6\right\}$ as $R=\left\{\left(x,y\right):y\right.$ is divisible by$\left.x\right\}$ is

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 the set $\left\{1,2,3,4,5,6\right\}$ as $R=\left\{\left(a,b\right):b=a+1\right\}$ is

Let $A=\{7,8,9\}$ and relation $R$ on set $A$ as $R=\left\{\left(x,y\right);|x-y|=6\right\}$.Check whether the relation $R$ is an empty relation or not. Explain your answer.

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 $A=\{7,8,9\}$ 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 $A=\{4,5,6\}$ 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.

The relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R=\left\{\right(a,b):|a-b|$ is even}, is

Let $R$ be a relation on the set of all real numbers defined by $aRb$ if $\left|a-b\right|\le \frac{1}{2}$. Then relation $R$ is

Assume $\mathrm{R}$ and $\mathrm{S}$ are (non-empty) relations in a set $\mathrm{A}$. Which of the following relation given below is false

Let $R_1=\left\{\left(a, b\right): a^2+b^2=4; a,\mathit{ }b\in R\right\}$, then relation $R_1$ is

Let $M$ be a set of $\left(2\times 2\right)$ non-singular matrices and $R$ be a relation defined on set $M$ such that $R=\{\left(A,B\right);A,B\in M;A$ is inverse of $B\}$ then $R$ is

Let $A=\left\{2, 3, 4, 5\right\}$ be a set and $R=\left\{\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right),\left(2,3\right),\left(3,2\right),\left(3,5\right),\left(5,3\right)\right\}$ be a relation on set $A$. Then $R$ is