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Boolean algebra

  1. Sep 13, 2005 #1

    Tony11235

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    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.
     
    Tony11235, Sep 13, 2005
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  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?)
     
    Hurkyl, Sep 14, 2005
  4. Sep 14, 2005 #3

    Tony11235

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    Would a truth table work?
     
    Tony11235, Sep 14, 2005
  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.
     
    David, Sep 14, 2005
  6. Sep 14, 2005 #5

    Hurkyl

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    Have you done anything on this problem, or just sit and stared at it?
     
    Hurkyl, Sep 14, 2005
  7. Sep 14, 2005 #6

    Tony11235

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    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.
     
    Tony11235, Sep 14, 2005
  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:
     
    Hurkyl, Sep 14, 2005
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