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How Do I Prove This Tautology?

  1. May 26, 2013 #1
    1. The problem statement, all variables and given/known data

    [ (p or r) & (not(p) or r) ] ---> r is a tautology. Prove this without using truth tables.

    2. Relevant equations

    See above. not(p) = !p = p' = the opposite value of p and ---> is an implication.

    3. The attempt at a solution

    I have made some prior simplification, and that is what I have at present. I don't know where to go from here. Expanding the terms seems to make things too complicated. Is there a shorter way?

    Any help would be greatly appreciated!
     
  2. jcsd
  3. May 26, 2013 #2
    Nevermind, I've solved it! For anyone interested in the solution, I just had to distribute the implication and then expanding was a lot quicker!
     
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