# Set theory with functions

• Jan 30th 2010, 05:42 PM
umbrella
Set theory with functions
Hello there,

I have the following assignment that my teacher gave me:

Let $\displaystyle X = {0,1,2,3,4}$ and the function $\displaystyle f: X \rightarrow X$ be $\displaystyle f(x) = (x^{3} - 2 \cdot x + 4) mod 5$.

Give a directed graph of $\displaystyle h$.

Okay I've drawn that one, it looks like this: see below

Give a directed graph of $\displaystyle h \circ h$.

I've that one too: see below
Give a directed graph of $\displaystyle (h \circ h) \oplus h$

How should I draw this one??? Is it like drawing one with the following relation set: $\displaystyle R = {(0,0), (1,0), (2,0), (3,4), (4,4), (0,4), (1,3), (2,3), (3,0), 4,0)}$?

now the next question is whether this $\displaystyle (h \circ h) \oplus h$ a function is. I have no idea, I guess it can be a function. But I need to argument that, which I can't... can somebody help me out with this?

If I've made some mistakes up there, can somebody please correct me?

Thanks! If you have any tips or any notation style that I can adapt, please give me a suggestion ^^!

Thanks for everything and your time,

Umbrella

PS: somehow my curly braclets don't work in Latex, how can I fix that :(?

My image: http://img163.imageshack.us/img163/1818/imag0039yn.jpg