The number of binary operations on the set 1, 2, 3 is _________? - Vidyadip

MCQ

The number of binary operations on the set {1, 2, 3} is _________?

✓
$3^9$
B
$9^3$
C
$27$
D
$3!$

✓

Answer

Correct option: A.

$3^9$

$3^9$

Solution:
Let us denote this set by S, then ∣S∣ = 3.
A binary relation defined on the elements of S maps all elements in S × S to elements in S by definition.
In this case any binary relation will thus have 32 = 9 inputs each of which is an ordered pair of elements from S and only 3 number of possible outputs.
If all possible binary operations are considered then it is possible to assign any of the 3 outputs to any of the 9 inputs. So the number of all binary operations would exactly be $3^9$.

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 "MCQ" from SETS→SETS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $a,\;b,\;c$ are the positive integers, then $(a + b)(b + c)(c + a)$ is

If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = $

Which axis is known as imaginary axis in argand plane?

Find the mean deviation about the mean for the data.

Height in cms	Number of boys
$95-105$	$9$
$105-115$	$13$
$115-125$	$26$
$125-135$	$30$
$135-145$	$12$
$145-155$	$10$

The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if

Which of the following is not a statement:

The negation of q ∨ ∼(p ∧ r) is.

If $\mathrm{S}=\left\{\mathrm{z} \in \mathbb{C}: \frac{\mathrm{z}-i}{\mathrm{z}+2 i} \in \mathbb{R}\right\}$, then :

A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If $L$ also intersects the $x$-axis, then the equation of $L$ is

If the coefficients of ${x^7}$ and ${x^8}$ in ${\left( {2 + \frac{x}{3}} \right)^n}$ are equal, then $n$ is