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