Relations practice · Medium

If $A=\left\{x \in z^{+}: x<10\right.$ and $x$ is a multiple of 3 or 4$\}$, where $z^{+}$is the set of positive integers, then the total number of symmetric relations on $A$ is

The relation R defined on the set of natural numbers as {(a,b):a differs from b by 3} is given by

$R$ is a relation from $\{11,12,13\}$ to $\{8,10,12\}$ defined by $y=x-3$. The relation $R^{-1}$ is

A relation on the set $A=\{x:|x| < 3, x \in Z\}$, where $Z$ is the set of integers is defined by $R=\{(x, y): y=|x|, x \neq-1\}$. Then the number of elements in the power set of $R$ is:

Let $R$ be a relation defined on $N$ as a $R b$ if $2 a+3 b$ is a multiple of $5, a, b \in N$. Then $R$ is

Let $R=\left\{(x, y): x^2+y^2=1\right.$ and $\left.x, y \in R\right\}$ be a relation in $R$. The relation $R$ is

$R=\{(a, b): 2 a+3 b$ is divisible by 5 and $a, b \in N\}$ is

If $R$ be a relation < from $A=\{1,2,3,4\}$ to $B=\{1,3,5\}$ i.e., $(a,b) \in R \Leftrightarrow a < b$, then $R^\circ {R^{ - 1}}$ is:

If two sets $A$ and $B$ are having 99 elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are

With reference to a universal set, the inclusion of a subset
in another, is relation, which is?

The relation $R$ defined on the set $A=\{1,2,3,4,5\}$ by $R=\left\{(x, y):\left|x^2-y^2\right|<16\right\}$ is given by

The relation $\leq$ on numbers has the following properties.

(i) $a \leq a \, \forall \, a \in {R}$ (Reflexivity)

(ii) If $a \leq {b}$ and ${b} \leq a$ then $a={b} \, \forall \, a, {b} \in {R}$ (Antisymmetry)

(iii) If ${a} \leq {b}$ and ${b} \leq {c}$ then $a \leq {c} \, \forall \, a, {b} \in {R}$ (Transitivity)

Which of the above properties the relation $\subset$ on ${p}({A})$ has?

The relation $R$ defined on the set $N$ of natural numbers by $x R y \Leftrightarrow 2 x^2-3 x y+y^2=0$ is

A relation $R$ from $C$ to $R$ is defined by $x R y$ iff $|x|=y$. Which of the following is correct?

Let $A$ be a non-empty set such that $A \times A$ has 9 elements among which are found $(-1,0)$ and $(0,1).$ Then,

A relation $R$ is defined over the set of non- negative integers as $x R y \Rightarrow x^{2}+y^{2}=36$ what is $\mathrm{R}$ ?

If $n(A)=3$, and $n(B)=4$, then $n(A \times A \times B)$ is equal to

A relation $R$ from $\mathbb{C}$ to $\mathbb{R}$ is defined by $x R y$ iff $|x|=y$. Which of the following is correct?

In the set ${N}$ of natural numbers, define the binary operation $*$ by $m * {n}=\operatorname{GCD}({m}, {n}), {m}, {n} \in {N}$. Then, which of the following is true?

I. $*$ is not a binary operation

II. $*$ is a binary operation

III. Inverse of each element of ${N}$ exist

IV. Inverse of each element of ${N}$ does not exist

Let $X=\{1,2,3,4,5\}$ and $Y=\{1,3,5,7,9\}$. Which of the following is not a relation from $X$ to $Y$ ?

If $R$ is a relation from a set $A$ to the $\operatorname{set} B$ and $S$ is a relation from $B$ to $C$, then the relation $S \circ R$

Which of the following statements is not correct for the relation R defined by aRb, if and only, if b lives within on kilometre from a?

If a set has 13 elements and $R$ is a reflexive relation on $A$ with $n$ elements, then

Let $A=\{1,2,3\}, B=\{1,3,5\}$. If relation $R$ from $A$ to $B$ is given by $\{(1,3),(2,5),(3,3)\}$, then $R^{-1}$ is

Let a relation $R$ be defined by $R=\{(4,5),(1,4),(4,6),(7,6),(3,7)\}$. The relation $R^{-1} o R$ is given by

Assume $\mathrm{R}$ and $\mathrm{S}$ are (nonempty) relations in a set $A$. Which of the following relation given below is false