Types of Relations

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 $A=\{a, b, c\}$ 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 $S$ 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

If we define a relation $R$ on the set $N\times N$ as $\left(a,b\right) R \left(c,d\right)\iff a+d=b+ c$ for all $\left(a,b\right),\left(c,d\right)‎\in ‎N\times N,$ then the relation is

Let $R$ is a relation defined as $R=\left\{\left(1, 2\right), \left(2, 3\right), \left(3, 4\right)\right\}$. The minimum number of ordered pairs which should be added to make relation $‘R’$ equivalence relation, are

Let $R$ is a relation defined as $R=\left\{\left(1,2\right),\left(2,3\right),\left(3,4\right)\right\}$ . The minimum number of ordered pairs which should be added to make relation $‘R’$ equivalence relation, are

Consider set $A=\left\{1,2,3\right\}.$ Number of symmetric relations that can be defined on $A$ containing the ordered pair $\left(1, 2\right)$ and $\left(2, 1\right)$ is

The relation $S=\left\{\left(3, 3\right),\left(4,4\right)\right\}$ on the set $A=\left\{3, 4, 5\right\}$ is ________.

Let $R=\left\{\left(3, 3\right),\left(6, 6\right),\left(9, 9\right),\left(12, 12\right),\left(6, 12\right),\left(\mathrm{3,9}\right),\left(3, 12\right),\left(3, 6\right)\right\}$ be a relation on the set $A=\left\{3,6,9,12\right\}$. The relation is

Let $A=\left\{p,\mathrm{ }q,\mathrm{ }r\right\}$ . Which of the following is an equivalence relation on $A$

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