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 

On the set $N$ of all natural numbers define the relation $R$ by $aRb$ if and only if the $\mathrm{GCD}$ of $a$ and $b$ is $2$, then $R$ is

The relation $R=\{\left(1, 1\right), \left(2, 2\right), (3, 3\left)\right\}$ on the set $\left\{1, 2, 3\right\}$ is

On the set $N$ of all natural numbers define the relation $R$ by $aRb$ if and only if the $\mathrm{GCD}$ of $a$ and $b$ is $2$, then $R$ is

Let $R$ be a relation over $N \times N$ and it is defined by $\left(a, b\right) R \left(c, d\right)⟺ a+d=b+c.$ Then $R$ is

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.

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

If $N$ denotes the set of all natural numbers and $R$ be the relation on $N\times N$ defined by $\left(a,b\right) R\left(c,d\right)$ and if $ad\left(b+c\right)=bc\left(a+d\right)$, then $R$ is

Let $P\mathit{=}\left\{\left(x\mathit{,}\mathit{ }y\right)\mathit{/}{x}^2\mathit{+}{y}^2\mathit{=}\mathit{1}\mathit{,}x\mathit{,}y\in R\right\}$. Then, $P$ is not

If a relation $R$ defined on a non-empty set $A$ is an equivalence relation, then $R$

$x^2=xy$ is a relation, which is

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

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 $R$ 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

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