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Boolean algebra

  1. Feb 9, 2010 #1
    why does a' * a' = a' ??

    this isn't a homework problem, but i am just wondering why because i used this to simplify another boolean equation. oh, and what's the difference between a' * a' and (a')' ? how do you even get (a')'?? confused :\
     
  2. jcsd
  3. Feb 9, 2010 #2
    Every element in a Boolean algebra is idempotent: [tex]xx = x[/tex] for every [tex]x[/tex].

    [tex]a'a'[/tex] is the product of [tex]a'[/tex] with itself; [tex](a')' = a[/tex] is [tex]a[/tex] complemented twice. Complement twice is the identity (complement is an involution).
     
  4. Feb 9, 2010 #3
    Make a truth table to see why.
    X can equal only 1 or 0 thus the truth table for x*x is below :
    --------
    x x x*x
    0 0 0
    1 1 1
    -------

    As you see if X = 0, then X*X = 0 = X, and if X = 1, then X*X = 1 = X. Thus X*X = X
     
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