# Homework Help: List all the functions from the three-element set

1. Sep 14, 2008

### sampahmel

Dear all,

List all the functions from the three-element set {1,2,3} to the set {a,b}.

The answer I have is 6 functions. However, the answer given at the back of the book has 24 functions:

Note: In the following functions, I will use (sub 1) denoting subscript 1.

f (sub 1) (1)=a , f (sub 1) (2)=a , f (sub 1) (3)=a
f (sub 2) (1)=a , f (sub 2) (2)=a , f (sub 2) (3)=b
f (sub 3) (1)=a , f (sub 3) (1)=b , f (sub 1) (1)=a
f (sub 4) (1)=a , f (sub 4) (1)=b , f (sub 4) (1)=b
f (sub 5) (1)=b , f (sub 5) (1)=a , f (sub 5) (1)=a
f (sub 6) (1)=b , f (sub 6) (1)=a , f (sub 6) (1)=b
f (sub 7) (1)=b , f (sub 7) (1)=b , f (sub 4) (1)=a
f (sub 8) (1)=b , f (sub 8) (1)=b , f (sub 8) (1)=b

2. Sep 16, 2008

### sampahmel

Re: Functions (urgent)

I think I did not make myself clear in the above thread.

I would like to know why are there 8 functions?

3. Sep 16, 2008

### Dick

Re: Functions (urgent)

There are 8 functions. 8=2^3. If the book says there are 24, it's quite wrong.