Question

Let A be a finite set containing 3 elements, then the number of functions from A to A is *


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Answer 1

Given :  A be a finite set containing 3 elements

To find : number of functions from A to A

Solution:

let say

A  = { 1 , 2 , 3}

A x A  = { ( 1, 1) , ( 1, 2) , ( 1, 3 ) , ( 2, 1) , ( 2, 2) , ( 2, 3) , ( 3 ,1 ) , ( 3, 2) , ( 3, 3) }

= 9 elements in A

Each element either can be presented in function or not

hence there are 2 ways to select each element

Hence total number of functions from A to A = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

= 2⁹

= 512

number of functions from A to A is 512

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