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Boolean algebra

  1. Sep 13, 2005 #1
    With [tex] x \oplus y [/tex] defined to be (here I'm using x' as the complement of x) xy'+x'y, prove [tex] x(y \oplus z) = xy \oplus xz [/tex]

    I'm stuck. Any hint or help would be great.
     
  2. jcsd
  3. Sep 14, 2005 #2

    Hurkyl

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    Well, what have you done so far?

    (I presume xy is the "and" operation, and x+y is the "or" operation?)
     
  4. Sep 14, 2005 #3
    Would a truth table work?
     
  5. Sep 14, 2005 #4

    David

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    You can just expand out both expressions and see they are the same. You will need to use de Morgan's laws to turn the complement of a product into a sum of complements, however. That is the only tricky part.
     
  6. Sep 14, 2005 #5

    Hurkyl

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    Have you done anything on this problem, or just sit and stared at it?
     
  7. Sep 14, 2005 #6
    I expanded the right side, thought deeply about it, tried a few other moves, but came up short and had to turn it in unfinished. Oh well, one low homework score won't kill me.
     
  8. Sep 14, 2005 #7

    Hurkyl

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    Well, if you had showed what you had done, maybe we could have pointed out the key step you were missing. Oh well. :frown:
     
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