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Math Help - A very annoying and simple logic derivation problem.

  1. #1
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    A very annoying and simple logic derivation problem.

    Hello everyone!

    Right, I know I'm overlooking something really simple here, and it frustrates me a lot.

    My primary assumption is:

    ~A v B

    and I want to derive:

    A ⊃B

    I started of with a sub-goal analysis method, then got stumped fairly quickly.
    I then tried to start from the top top...
    In short, what can you derive from '~A v B'? As far as I know, without any other information you can't derive anything at all... but to solve this derivation, surely you must derive something from it?

    It seems like it should be such a simple derivation as well, what am I ignorantly missing?

    Thanks a bunch chaps.
    Last edited by mr fantastic; January 14th 2009 at 09:48 PM. Reason: Language modification
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  2. #2
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    Well we do know the \neg A \vee B \equiv A \to B \equiv \neg B \to \neg A.
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  3. #3
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    Thanks for the fast reply Plato.

    I'm afraid I only know Sentential Logic, and unless it's written out in a way I haven't yet seen, I don't think that's SL. I'm still confused as to what the first step would be... disjunction elimination? Biconditional introduction?
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  4. #4
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    Quote Originally Posted by Freols View Post
    I'm afraid I only know Sentential Logic, and unless it's written out in a way I haven't yet seen, I don't think that's SL. I'm still confused as to what the first step would be... disjunction elimination? Biconditional introduction?
    The statement that not A or B is equivalent to A implies B is equivalent to not B implies not A.
    The proofs of these are most easily done with truth tables.
    I guess that I really do not know exactly what you are asking notwithstanding having taught logic for years.
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  5. #5
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    not quite sure if this is the kind of thing you are looking for, but with the premise -A or B, one can prove A -> B via the conditional introduction rule. Thus when you assume A, this implies --A (via some sort of double negation rule), and this in turn implies B (via your initial premise and a disjunction-elimination rule).
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