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

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

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

The relation $R$ defined on the set $N$ of natural numbers given by $\left\{\left(x,y\right): x^2-3xy+2y^2=0, \forall x,y\in N\right\}$ 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

Let $\mathrm{N}$ represent the set of natural numbers, and a relation $\mathrm{R}$ in the set $\mathrm{N}$ of natural numbers be defined as $(\mathrm{x},\mathrm{y})\iff {\mathrm{x}}^2-8\mathrm{xy}+7{\mathrm{y}}^2=0$ $\forall \mathrm{x}$. $\mathrm{R}$ is a $\_\_\_\_\_\_\_\_\_\_\_$ relation. (Choose the option that fits the blank)

A relation $R$ is defined in the set of real numbers as $xRy$, if $x^2=xy$. Then this relation $R$ is

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

Consider the following relation $R$ on the set of real square matrices of order $3$, $R=\left\{\right(A,B\left)\right|AB=BA\}$

STATEMENT-1: Relation $R$ is equivalence.

STATEMENT-2: Relation $R$ is symmetric.

Which of the following is correct.

A relation $R$ is defined as $\left(x,y\right)\in R\Rightarrow x^y=y^x$ for $x, y\in I-\left\{0\right\}$, where $I$ is the set of all integers. Then the relation $R$ is: