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Logics Problem

  1. May 8, 2005 #1
    Hi, I am having trouble showing that
    {F > ~ G. ~ F > ~H, (~ F v G) & H}
    is inconsistent in SD.

    Also I don't understand how one can derive: ~ H
    from: {(R v ~ H), (~ R v ~ H)}


    I would be grateful to anyone who can help me understand these problems.
     
  2. jcsd
  3. May 8, 2005 #2
    For both you need to make provisional assumptions and show that either the assumption yields an inconsistency in the proof (introduced by the assumption) or validates it. For #2, I would make the assumption R.
     
  4. May 9, 2005 #3

    honestrosewater

    User Avatar
    Gold Member

    If you still have trouble, here's a few step to get you started:
    1. F -> ~G
    2. ~F -> ~H
    3. (~F v G) & H
    4. ~F v G [3, Simplification]
    5. ~F v ~G [1, Implication]
    6. (~F v G) & (~F v ~G) [4, 5, Conjunction]
    7. ~F v (G & ~G) [6, Distribution]
    8. ... assumption time

    1. R v ~H
    2. ~R v ~H
    3. (R v ~H) & (~R v ~H) [1, 2, Conjunction]
    4. ... does 3 look familiar?
     
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