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Symbolic logic question

  1. Dec 5, 2007 #1
    1. The problem statement, all variables and given/known data
    I need to prove that (A & ~A) > (B & ~B) is a theorem of sentential derivation. (I'm using '>' to indicate a conditional connective.) Basic rules of SD (&I, &E, >I, >E, etc.) are what I can use, and I don't think I can use SD+ rules like modus tollens, etc.


    2. Relevant equations



    3. The attempt at a solution
    I'm assuming that I can start with 'A & ~A' as an initial auxiliary assumption on line 1. I'm not sure, though, if I should put B as a further auxiliary assumption with its own scope line on line 3, and then try to use negation introduction and &I to derive 'B & ~B', and then end the derivation with >I to get the theorem.
    Any help for a confused linguistics student would be greatly appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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