Is it possibe to have A proves B and not A proves B I'm tending towards thinking you can't, but not sure why. Any ideas?
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Originally Posted by NYC Is it possibe to have A proves B and not A proves B I'm tending towards thinking you can't, but not sure why. Any ideas? I'm not sure what you mean by "proves". If you mean implies then the answer is yes. p q p-->q T T T T F F F T T F F T
Originally Posted by NYC Is it possibe to have A proves B and not A proves B I'm tending towards thinking you can't, but not sure why. Any ideas? No (at least as I read your question). But here's a valid sequent you might consider. A->B, ~A->B |- B or alternatively, |- (A->B) -> ((~A->B) -> B), or getting conjunction into the "equation", |- ((A->B) & (~A->B)) -> B
Is it possibe to have A proves B and not A proves B This is possible iff B is provable by itself.
Originally Posted by emakarov This is possible iff B is provable by itself. Thanks In this case is B a tautology?
Originally Posted by NYC Thanks In this case is B a tautology? You betcha!
Originally Posted by oldguynewstudent You betcha! Thanks for the quick response! How would you show that B is a tautology?
Originally Posted by NYC Thanks for the quick response! How would you show that B is a tautology? That would depend on B. Do you have the example of your actual problem?
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