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Boolean Arithmetic Simplification

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data

    I am asked to prove that [itex](\sim x)\vee z = \sim(x\vee y)\vee\sim(y\vee\sim z)\vee\sim(x\vee\sim y)\vee\sim(\sim y\vee\sim z)[/itex].

    I've tried using all combinations of DeMoran's rule, the distributive rule to get the y terms together, and the absorption rule to get rid of the y (which is required in order to simplify it down in terms of x and z.


    2. Relevant equations

    DeMorgan's Rule: [itex]\sim(p\wedge q) = \sim p\vee\sim q[/itex]
    Absorption Rule: [itex]p\vee(p\wedge q) = p[/itex]

    3. The attempt at a solution

    I can post some of the steps I've taken, but none really lead anywhere. Where is a good place to start for a question like this?
     
  2. jcsd
  3. Sep 26, 2011 #2

    NascentOxygen

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    Staff: Mentor

    Convert the OR's contained within brackets to AND's using DeMorgan's rules.
     
  4. Sep 26, 2011 #3
    Thanks -- yeah, I was trying that before, but couldn't get it simplified down enough.

    I got the solution now (and it wasn't too hard). I just had to use DeMorgan's and the distributive rule to get rid of all the Ys first, and then everything else just fell into place without much effort.
     
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