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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

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

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