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.

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

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

Let $S$ be the set of all real numbers and let $R$ be a relation on $S$ defined by $a R b \iff a^2+b^2=1$. Then, $R$ is

Let $S$ be the set of all straight lines in a plane. Let $R$ be a relation on $S$ defined by $a R b \iff a\perp b$. Then, $R$ is