Thread: Help with functions given 2 sets

I am working on a homework assignment for school. I am having problems with my homework. I have started to work out the question, but I seem to be getting stuck. I am not sure if what I have is correct or not. This is the question that I am currently working on.


Question: Let A={1,2,3,4} and B={x,y,z}
a) List the five functions from A to B.
b) How many functions f: A -> B are there?
c) How many functions f: A -> B are one-to-one?
d) How many functions g: B -> A are there?


Answers:
a) I have only been able to come up with 3 functions. I thought of the functions as having ordered pairs so I came up with this as an answer.
f(A) = {(1,x), (2,y). (3,z), (4,x)}
f(A) = {(1,y), (2,z), (3,x), (4,y)}
f(A) = {(1,z), (2,x), (3,y), (4,z)} from here I am not sure of what the last two functions would be. Also not sure if this is the correct way to solve this problem.


b) I came up with the answer 3^4 to equal 81 functions
c) I came up with there are no one-to-one functions
d) I came up with 4^3 to equal 64 functions

Originally Posted by needhelp101

I am working on a homework assignment for school. I am having problems with my homework. I have started to work out the question, but I seem to be getting stuck. I am not sure if what I have is correct or not. This is the question that I am currently working on.


Question: Let A={1,2,3,4} and B={x,y,z}
a) List the five functions from A to B.
b) How many functions f: A -> B are there?
c) How many functions f: A -> B are one-to-one?
d) How many functions g: B -> A are there?


Answers:
a) I have only been able to come up with 3 functions. I thought of the functions as having ordered pairs so I came up with this as an answer.
f(A) = {(1,x), (2,y). (3,z), (4,x)}
f(A) = {(1,y), (2,z), (3,x), (4,y)}
f(A) = {(1,z), (2,x), (3,y), (4,z)} from here I am not sure of what the last two functions would be. Also not sure if this is the correct way to solve this problem.


b) I came up with the answer 3^4 to equal 81 functions
c) I came up with there are no one-to-one functions
d) I came up with 4^3 to equal 64 functions

They are correct.

My functions so far for part A are correct? If that is the case, I am unsure of how to find the last 2 functions. The question is asking for 5 functions, but I only have 3.

Originally Posted by needhelp101

My functions so far for part A are correct? If that is the case, I am unsure of how to find the last 2 functions. The question is asking for 5 functions, but I only have 3.

How about: $\{(1,x),(2,x),(3,x),(4,x)\}~\&~\{(1,x),(2,x),(3,x ),(4,y)\}$

Oh wow. That just makes me feel dumb. I'm not sure why I was thinking that I could not do that. Thanks. Also, my other answers look correct? And the way that I am saying that these are functions are correct? For example, the 3 functions that I came up with f(A) is correct? Or would I have to write it out as f: (A -> B) = {....}?