How many reflexive relation are there on a set ' with 3 elements - Vidyadip

MCQ

How many reflexive relation are there on a set ' with $3$ elements

A
${2^3}$
✓
${2^6}$
C
${2^9}$
D
${2^{12}}$

✓

Answer

Correct option: B.

${2^6}$

b
Total reflexive relation on a set with $\mathrm{n}$

elements is $2^{n^{2}-n}$

Here $n=3$

$\therefore 2^{3^{2}-3}=2^{6}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $R$ be the relation on the set $A = \{1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)\}.$ Then,

Let $f(\mathrm{x})=\left\{\begin{array}{cl}-\mathrm{a} & \text { if }-\mathrm{a} \leq \mathrm{x} \leq 0 \\ \mathrm{x}+\mathrm{a} & \text { if } 0<\mathrm{x} \leq \mathrm{a}\end{array}\right.$ where $\mathrm{a}>0$ and $\mathrm{g}(\mathrm{x})=(f|\mathrm{x}|)-|f(\mathrm{x})|) / 2$. Then the function $\mathrm{g}:[-\mathrm{a}, \mathrm{a}] \rightarrow[-\mathrm{a}, \mathrm{a}]$ is

The corner points of the feasible region determined by the system of linear constraints are $(0,10),(5,5),(15,15),(0,20)$. Let $Z=p x+q y$, where $p, q>0$. Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(15,15)$ and $(0,20)$ is

On the interval $[0, 1],$ the function ${x^{25}}{(1 - x)^{75}}$ takes its maximum value at the point

Let $A=\left(\begin{array}{rrr}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)$ and $B=7 A^{20}-20 A^{7}+2 I$, where $I$ is an identity matrix of order $3 \times 3$ If $B=\left[b_{i j}\right]$, then $b_{13}$ is equal to $....$

Let $O$ be the origin, and $\mathrm{M}$ and $\mathrm{N}$ be the points on the lines $\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$ and $\frac{\mathrm{x}+8}{12}=\frac{\mathrm{y}+2}{5}=\frac{\mathrm{z}+11}{9}$ respectively such that $\mathrm{MN}$ is the shortest distance between the given lines. Then $\overrightarrow{\mathrm{OM}} \cdot \overrightarrow{\mathrm{ON}}$ is equal to ..................

A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a $5$ or $6$ in the dice is

The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively. If $P(X=1)=\frac{4}{243}$, then $P ( X =4$ or $5)$ is equal to.

Let the image of the point $P (1,2,3)$ in the line $L : \frac{ x -6}{3}=\frac{ y -1}{2}=\frac{ z -2}{3}$ be $Q .$ let $R (\alpha, \beta, \gamma)$ be a point that divides internally the line segment $PQ$ in the ratio $1: 3$. Then the value of $22(\alpha+\beta+\gamma)$ is equal to

$\int\limits_0^\pi {} $ $(x · sin^2x · cos x) dx $ =