Types of Relations

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.

Write the identity relation on set $A=\{2,3,4\}$.

Write the identity relation on set $A=\{7,8,9\}$.

Check whether the following relation $R=\left\{\left(1,1\right),\left(2,2\right)\right\}$ on set $A=\left\{1,2\right\}$ is an identity relation or not. Explain.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff xy>4$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff xy<3$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff xy>3$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff x+y>3$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff x+y\le 3$ such that $x\in A \& y\in B$.

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 $R$ be a reflexive relation on a set $A$and $I$ be the identity relation on $A$. Then

Let $R$be a reflexive relation on a set $A$and $I$ be the identity relation on$A$. Then