Question

What is the total number of functions that can be defined from the set {1,2} to the set {1,2,3}?​

Answer 1

The total number of functions that can be defined from the set {$1,2$} to the set {$1,2,3$} is $3^{2} =9.$

Step-by-step explanation:

Given:

set 1 ={$1,2$}

set 2={$1,2,3$}

To find:

The total number of functions can be defined from set 1 to set 2.

Solution:

Set 1= {$1,2$}

Set 2={$1,2,3$}

Number of elements in set 1 = $m$

Number of elements in set 2=  $n$

Here, $m=2$

$n=3$

Number of functions from set 1 to set 2 = $n^{m}$

                                                                 = $3^{2}$

 ⇒Numer of functions from set 1 to set 2$= 9$

So the final answer is $9$