If A = 1, 2, 3 , show that a onto function f : A → A must be one-… - Vidyadip

Question

If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.

✓

Answer

A = {1, 2, 3}
Possible onto function from A to A can be the following:

{(1, 1), (2, 2), (3, 3)}
{(1, 1), (2, 3), (3, 2)}
{(1, 2), (2, 2), (3, 3)}
{(1, 2), (2, 1), (3, 3)}
{(1, 3), (2, 2), (3, 1)}
{(1, 3), (2, 1), (3, 2)}

Here, in each function, different elements of the domain have different images.
Therefore, all the function are one-one.

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 "3 Marks Question" from Functions→Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find2B + 3A and 3C - 4B.

Let $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}$ and $\vec{\text{c}}=\text{c}_1\hat{\text{i}}+\text{c}_2\hat{\text{j}}+\text{c}_3\hat{\text{k}}.$ Then,
If $C_2 = -1$ and $C_3 = 1$, show that no value of $C_1$ can make $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ coplanar.

A bag contains 8 red and 6 green balls. Three balls are drawn one after another without replacement. Find the probability that at least two balls drawn are green.

Evaluate the following integrals:
$\int\frac{\cos\text{x}-\sin\text{x}}{1+\sin2\text{x}}\text{dx}$

Show that $\frac{\text{logx}}{\text{x}}$ has a minimum value at x = e.

Find the vector equation of the plane with intercepts 3, -4 and 2 on x, y and z-axis respectively.

A coin is tossed three times, if head occurs on first two tosses, find the probability of getting head on third toss.

If A and B are events such that P(A) = 0.6, P(B) = 0.3 and $\text{P}(\text{A}\cap\text{B})=0.2$ find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ and $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big).$

Evaluate the following integrals:
$\int\frac{1}{(\text{x}-1)\sqrt{\text{x}^2+1}}\text{ dx}$

Find the principal value of the following:
$\cos^{-1}\Big(-\frac{\sqrt3}{2}\Big)$