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Math Help - Derive ~A

  1. #1
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    Derive ~A

    Derive: ~A

    1| A⊃(~BVC) ASS
    2| B ASS
    3| A⊃~C ASS
    ------------------

    So far I have:

    1| A⊃(~BVC) ASS
    2| B ASS
    3| A⊃~C ASS
    4| |A ASS / ⊃E
    5 |~BVC 1,4 ⊃E


    I know I need to derive a contradiction to get ~A, and I see it hiding in ~B and B, and ~C and C, but I can't seem to get it out of those last lines...Any help would be appreciated! (and i'll hit the thank you button )
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  2. #2
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    Re: Derive ~A

    Assume A. Then ~B \/ C from 1. Also, ~C from 3. Using disjunction elimination on ~B \/ C, assume ~B. This gives a contradiction with B. Similarly, assume C. This gives a contradiction with ~C. Thus, we get a contradiction from assuming A.
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