How many reflexive relations are possible in a set A whose n(A)=3… - Vidyadip

MCQ

How many reflexive relations are possible in a set $A$ whose $n(A)=3$ ?

✓
$2^6$
B
$2^9$
C
$2^3$
D
8

✓

Answer

Correct option: A.

$2^6$

(a) : Number of reflexive relations on a set having $n$ elements $=2^{n(n-1)}$
So, required number of reflexive relations $=2^{3(3-1)}=2^6$

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 Relations and Functions→Relations and Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of the integral ${\int_{ - 1/2}^{1/2} {\left[ {{{\left( {\frac{{x + 1}}{{x - 1}}} \right)}^2} + {{\left( {\frac{{x - 1}}{{x + 1}}} \right)}^2} - 2} \right]} ^{1/2}}dx$ is

$\int {\sqrt {1 + \sin \left( {\frac{x}{4}} \right)\,} } dx$

If the system of equations $x +y + z = 6$ ; $x + 2y + 3z= 10$ ; $x + 2y + \lambda z = 0$ has a unique solution, then $\lambda $ is not equal to

The equations of the line passing through the point $(1,2,-4)$ and perpendicular to the two lines $\frac{{x - 8}}{3} = \frac{{y + 19}}{{ - 16}} = \frac{{z - 10}}{7}$ and $\frac{{x - 15}}{3} = \frac{{y - 29}}{8} = \frac{{z - 5}}{{ - 5}}$, will be

If $a>0$ and discriminant of $a x^2+2 b x+c$ is negative, then $\triangle=\begin{vmatrix}\text{a}&\text{b}&\text{ax}+\text{b}\\\text{b}&\text{c}&\text{bx}+\text{c}\\\text{ax}+\text{b}&\text{bx}+\text{c}&0\end{vmatrix}$ is:

Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is

The trace of a square matrix is defined to be the sum of its diagonal entries. If $A$ is a $2 \times 2$ matrix such that the trace of $A$ is $3$ and the trace of $A^3$ is -$18$ , then the value of the determinant of $A$ is. . . . .

Let $\mathrm{A}=\{1,2,3,4,5\}$. Let $\mathrm{R}$ be a relation on $\mathrm{A}$ defined by $x R y$ if and only if $4 x \leq 5 y$. Let $m$ be the number of elements in $\mathrm{R}$ and $\mathrm{n}$ be the minimum number of elements from $\mathrm{A} \times \mathrm{A}$ that are required to be added to $\mathrm{R}$ to make it a symmetric relation. Then $m+n$ is equal to:

Area of the region between the curves $\text{x}^2+\text{y}^2=\pi,\text{y}=\sin\text{x}$ and $y-$axis in first quadrant is:

If $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then $(A + B)^{-1} =$