# Discreet Math question: Defining a boolean algebra on a set of function?

1. Apr 24, 2012

### pistolpete333

I have a question on my hw that asks me to

define a boolean algebra on set B where B = {f|f is a subset of integers squared and f is a function} I need to specify the operations, identity elements and show how to identify the complement elements.

I have tried, but am really not sure if I am going in the right direction. So far I have:
operations
+ for function addition (f + g)(x)
* for function composition (f o g)(x)
Identity Elements
Ix (or I sub x) the identity function, my reasoning is (f o Ix)(x) = f(x)
I cant figure out a second, but I was thinking like an empty function of some sort if there is such a thing

Compliment Elements
Inverse function (f^-1) reasoning is (f o f^-1) = Ix
I dont have another compliment element for this.

That is what I have so far and have no idea if I am on the right track or not, and my professor did not cover this topic well. If you could help me out or point me in the right direction that would be awesome. Let me know if any more info is needed