Types of Relations

If $\mathrm{A}=\left\{7, 8, 9\right\}$ and $\mathrm{R}$ is the relation on set $\mathrm{A}$, then find the antisymmetric relation on set $\mathrm{A}$.

In the set $\mathrm{N}$ of natural numbers, a relation $\mathrm{R}$ is defined by $\mathrm{aRb}\iff \mathrm{a}$ is a factor of $\mathrm{b}$. Examine if $\mathrm{R}$ is Anti-symmetric.

If $\mathrm{A}=\left\{\mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{s}\right\}$ and $\mathrm{R}$ is the relation on set $\mathrm{A}$, then find the antisymmetric relation on set $\mathrm{A}$.

If $\mathrm{A}=\left\{2, 3, 4, 5\right\}$ and $\mathrm{R}$ is the relation on set $\mathrm{A}$, then find the antisymmetric relation on set $\mathrm{A}$.

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

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 $S$ 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

Let $S$ be the set of all real numbers and let $R$ be a relation on $S$ defined by $a R b\iff \left|a\right|\le b$. Then, $R$ is

Let $R$ be a relation on the set $A$ of ordered pairs of positive integers defined by $\left(x, y\right) R \left(u, v\right)$ if and only if $xv=yu.$ Show that $R$ is an equivalence relation.

The number of reflexive relations of a set with four elements is equal to 

$R\subseteq A\times A$ (where $A\ne 0)$ is an equivalence relation if $R$ 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 $A=\left\{1,2,3,4\right\}$ and $R$ be a relation on $A$ given by $R=\left\{\left(1,1\right)\left(2,2\right)\left(3,3\right)\left(4,4\right)\left(1,2\right)\left(2,1\right)\left(1,3\right)\left(3,1\right)\right\}$ then $R$ is

Let $Z$ denote the set of all integers. If a relation $R$ is defined on $Z$ as follows:

$\left(x, y\right)\in R$ if and only if $x$ is multiple of $y,$ then $R$ is

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