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Tautalogical Consequence

  1. Sep 16, 2007 #1
    I am in needof help with the following problem:

    Premises : Cube(a) v Cube(b)
    Dodec(c) v Dodec(d)
    ~Cube(a) v ~Dodec(c)

    Conclusion: Cube(b) v Dodec(d)


    I need to add a sentence to the proof that is tautalogical consequence of two of the premises. I just can't see how to make such a deduction. Any help would be much appreciated
     
  2. jcsd
  3. Sep 16, 2007 #2
    well it's quite immediate if take into account material conditional and destructive dillema:
    ~cube(a)->cube(b)
    ~dodec(c)->dodec(d)
    ~Cube(a) v ~Dodec(c)
    so from DD you get the conclusion.
    but let's say for the sake of argument that you can't use it here, so:
    so what about ((Cube(a)vCube(b))->(Dodec(c)vDodec(d))->(~Cube(a)v~Dodec(c))->(Cube(b)vDodec(d))
    you only need to check that then next thing is a tautology, quite long:
    ((~P->Q)->(~R->S)->(P->R)->(~Q->~S))
    but as you might see it's all equivalent.
     
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