Proving the identity of boolean equations

Discussion in 'Homework Help' started by mcc123pa, Sep 12, 2010.

  1. mcc123pa

    Thread Starter Member

    Sep 12, 2010
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    0
    Hi everyone:

    I was assigned the following problem for homework:
    Y+X'Z+XY'=X+Y+Z

    The directions read: prove the identity of each of the following Boolean equations using algebraic manipulation.

    I have tried some various attempts, such as factoring out X and X' or Y and Y' but have not made any progress.

    Could someone please post the solution? Thanks!
     
  2. Georacer

    Moderator

    Nov 25, 2009
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    1,266
    There's a boolean identity saying that A+BC=(A+B)(A+C). Try to use that one.
    HINT: Try the first and third term to begin with.
     
  3. mcc123pa

    Thread Starter Member

    Sep 12, 2010
    40
    0
    Thanks so much for the hint! I think I figured it out!

    Is this correct? :

    y+x'z+xy'= x+y+z (original equation)

    (y+x)(y+y') (used the identity a+bc= (a+b)(a+c) as suggested)
    (y+x)(1) (used the identity y+y'=1)
    y+x+x'z =x+y+z (put the result of line three back into the original equation)
    (x+x')(z+x) which in turn equals (z+x)(I did the same step as lines 2&3)
    x+y+z=x+y+z (put the result from the line above back into the original equation)

    Please let me know. Thanks!!
     
  4. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Great! That's it! Just write your path of thoughts in sequential lines, like my post in this thread for example. (You don't have to use LaTex of course). It looks more official that way and is easier for people to follow.
     
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