Types of Relations

A relation $R$ on the set $A=\left\{a,b,c\right\}$is said to be symmetric if 

A relation $R$ is said to be reflexive for all $a,b\in A$, if  

A relation $R$ on set $A$ is said to be the identity relation if 

Let $R=\left\{\left(a,b\right):a \text{divides} b\right\}$ defined on set of natural numbers; then $R$ is

Let $R=\left\{\left(L_1,L_2\right):L_1 \text{is perpendicular to} L_2\right\}$ defined on the set of all lines in $XY-$plane, then $R$ is

$R=\left\{\left(x,y\right):x<y\right\}$ defined on $N$ is

Let $A=\left\{1,2,3\right\}$, and $R=\left\{\left(1,1\right),\left(2,1\right),\left(2,2\right),\left(1,2\right),\left(3,2\right),\left(3,3\right)\right\}$; then $R$ is:

Let $A=\left\{1,2,3\right\}$, and $R=\left\{\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(2,1\right),\left(2,3\right)\right\}$; then $R$ is:

Let $A=\left\{1,2,3\right\}$, which of the following is not an equivalence relation on $A?$

Let $R$ be the relation in the set $N$ given by $=R=\left\{\left(a,b\right):a=b-2, b⩾6\right\}$.

Choose the correct answer.

Let $R$ be the relation in the set $\left\{1,2,3\right\};$ given by $R=\left\{\left(1,2\right),\left(2,2\right),\left(1,1\right),\left(2,3\right),\left(1,3\right),\left(3,3\right),\left(3,2\right)\right\}.$ Choose the correct answer.

Let$R=\left\{\left(1,3\right),\left(2,4\right),\left(4,2\right),\left(2,3\right),\left(3,1\right)\right\}$ be a relationship on set $A=\left\{1,2,3,4\right\}$. The relation is 

Which of the following is not an equivalence relation on $Z?$

A relation $R$ on the set $A=\left\{a,b,c\right\}$ is said to be transitive, if

Let $R$ be the relation on the set $N$ of natural numbers defined by $a+3b=12.$ Find the domain of $R.$

Let $R$ be the relation on the set $N$ of natural numbers defined by $a+3b=12.$ Find $R.$

Let $A=\left\{1,2,3,5\right\}$ and $B=\left\{2,4,6,10\right\}$. Let $R=\left\{\left(a,b\right):a\in A,b\in B,a \text{divides} b\right\}$ be relation from $A$ to $B.$ Find $R,$ and show that domain of $R$ is $A$ and range of $R$ is $B.$

Let $A=\left\{2,3,4\right\}$ and $B=\left\{1,2,5,6\right\}$ and let $R=\left\{\left(a,b\right):a\in A,b\in B,a<b\right\}$ be relation from $A$ to $B.$ Find $R,$ the domain of $R$ and its range. What will be the relation of $a>b$ instead of $a<b.$

Find the identity relation on the set $A=\left\{5,6,7\right\}$

Let $A=\left\{1,2\right\}$ and $B=\left\{3,4\right\}$ and let $R=\left\{\left(a,b\right):a\in A,b\in B, a>b\right\}.$ Show that $R$ is an empty relation from $A$ to $B.$