Which functions are missing from {1,2,3} to {a,b} and why?

[Kingyou123]

Homework Statement

How many functions are there from {1,2,3} to {a,b}? Which are injective? Which are surjective?

Homework Equations

n^m. gives the number of functions

The Attempt at a Solution

To me the number of functions that can be made are 6 because 3x2=6 but I have read online that n^m, n being the elements in the second set and m being the number of elements in the first set, gives you the number of functions. That equation gives me 8 functions but for the life of me I can't figure which functions I'm leaving out.

Also there can't be any injective functions because f(1) can take 2 values and f(2) can take one value. Leaving f(3) with none so therefore It can't be injective,correct?

 

[SammyS]

Homework Statement

How many functions are there from {1,2,3} to {a,b}? Which are injective? Which are surjective?

Homework Equations

n^m. gives the number of functions

The Attempt at a Solution

To me the number of functions that can be made are 6 because 3x2=6 but I have read online that n^m, n being the elements in the second set and m being the number of elements in the first set, gives you the number of functions. That equation gives me 8 functions but for the life of me I can't figure which functions I'm leaving out.

You are missing two functions for which 1 → b .

View attachment 96266
Also there can't be any injective functions because f(1) can take 2 values and f(2) can take one value. Leaving f(3) with none so therefore It can't be injective,correct?

 

[Kingyou123]

You are missing two functions for which 1 → b .

Thank you, was my explanation for injective correct?

 

[SammyS]

Thank you, was my explanation for injective correct?

Yes

 

[Kingyou123]

Yes

Awesome thank you :)