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Messy Logic Problem

  1. Jan 10, 2008 #1
    Hi,

    Really struggling with this logic problem, would be very grateful to anyone willing to help

    A v D
    (~B ^ ~C) <==> D
    B ==> ~(C ==> A)
    ---------------------
    ~B

    Thanks in advance

    Hayden Kee
     
  2. jcsd
  3. Jan 11, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    What exactly do you want to do? Determine whether or not the argument is valid?

    What happens if you take A true, B true, C false, and D false?
     
  4. Jan 11, 2008 #3
    trying to derive the conclusion
    I did eventually work it out by assuming B and C to be true, after which I was able to show that D must be false, which allowed me to Eliminate the D v A disjunction showing that A is the result either way. Therefore I was left with C==>A which proved that my assumption of B must be false because of the third premise.

    Thanks,

    Hayden
     
  5. Jan 11, 2008 #4
    I've also assumed B and C, with the C sub-derivation ending with A, and the final three lines of the B sub-derivation ending with the following:
    W| C => A
    X| B => ~(C =>A)
    Y| ~(C =>A)

    This allows ~I for the conclusion of ~B through the B assumption (line 4), and the contradictory pair on lines W and Y:

    Z| ~B 4, W, Y, ~I

    What I can't figure out is how to get A on the C sub-derivation. :S
     
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