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Math Help - How to show that a given sentence is not a logical consequence of the given sentences

  1. #1
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    How to show that a given sentence is not a logical consequence of the given sentences

    If I am given 4 sentences:
    a) ...
    b) ...
    c) ...
    d) ...

    and a conclusion
    f) ...

    How can I show that f) is not a logical consequence of a), b), c) and d) ?
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  2. #2
    A Plied Mathematician
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    One way: assume the premises are true, the conclusion is false, and you don't get a contradiction. This is rather difficult to apply, however, since how do you know if have done enough work to show there is no contradiction? Still, it is valid, if you can achieve it.
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  3. #3
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    Quote Originally Posted by devouredelysium View Post
    If I am given 4 sentences:
    a) ...
    b) ...
    c) ...
    d) ...

    and a conclusion
    f) ...

    How can I show that f) is not a logical consequence of a), b), c) and d) ?
    Given an interpretation in which the four premises are true and the conclusion is false.
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