Equivalence 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 

Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\left\{\right(a,b)\in A\times A$ : $b=\left|a\right|$ or $\left.b^2=a+1\right\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is

The number of relations, on the set $\left\{1, 2, 3\right\}$ containing $\left(1, 2\right)$ and $\left(2, 3\right)$ which are reflexive and transitive but not symmetric, is _________.

Let $A=\{1,2,3,4,5,6,7\}$. Then the relation $R=\left\{\right(x,y)\in A\times A:x+y=7\}$ is

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

A relation $M$ is defined on set of real numbers.

$M=${$\left(a,b\right)/a,b\in R$ and $a+b$ is an irrational} then $M$ 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

$x^2=xy$ for real values of $x$ and $y$ is a relation which is

Let $A=\{a, b, c\}$ and the relation $R$ be defined on $A$ as follows:

$R=\left\{\right(a,a),(b,c),(a,b\left)\right\}$.

Then, write minimum number of ordered pairs to be added in $R$ to make $R$ reflexive and transitive.

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 $\mathrm{R}=\left\{(x,y):x,y\in \mathrm{N}\right.$ and $\left.x^2-4xy+3y^2=0\right\}$ where $\mathrm{N}$ is the set of all natural numbers. Then the relation $\mathrm{R}$ 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

Relation $R$ defined in set of real numbers by $R=\left\{(a, b):a\le b^3\right\}$ is

Let $S$ be the relation on $N$ defined by $S=\left\{\left(x,y\right): \frac{y}{2}\le x\le 2y\right\}$. Then, $S$ is

If $R$ and $S$ are two symmetric relations (not disjoint) on a set $A$, then the relation $R\cap S$ is

If $A=\{1, 2, 3, 4\}$, then a relation $R=\left\{\right(1, 1) ,(2, 2), \left(3, 3\right), (4, 4), (2, 4), (1, 3), (1, 4), (1, 2\left)\right\}$ on set $A$ is

Consider the following relations $R=\left\{\right(x, y)\mid x, y$ are real numbers and $x=wy$ for some rational number $w\}$
$S=\{\left(\frac{m}{n},\frac{p}{q}\right)$ where $m, n, p$ and $q$ are integers such that $n, q\ne 0$ and $qm=pn\}$. Then

The relation $R$ defined as $R=\left\{\left(x, y\right)\mid x+y=10, x, y\in \mathrm{N}\right\}$ is

For any two real numbers $\theta$ and $\varphi ,$ we define $\theta R\varphi$ as ${\sin }^2 \theta +{\cos }^2 \varphi =1,$ then relation $R$ is

If $R$ is a relation on the set $N$, defined by $\left\{\right(x,y):2x-y=10\}$, then $R$ is