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

  1. Apr 24, 2012 #1
    1. The problem statement, all variables and given/known data
    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
     
  2. jcsd
  3. Apr 25, 2012 #2

    tiny-tim

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