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Math Help - Deriving rules of inference

  1. #1
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    Deriving rules of inference

    I'm going over old test results, and for whatever reason I just can't get this one into my head.

    Given the proposition

    (p \rightarrow q)\rightarrow(p \vee r \rightarrow q \vee r)

    determine whether it is a tautology
    [it is, of course], and, if it is a tautology, write the valid argument determined by it.

    In other words, figure out what rule of inference can be derived from this argument. I believe it is modus tollens, but am not sure, and just can't see what method I would use to go about this. Any ideas?

    Thanks to all the good people out there!
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by epicurean View Post
    I'm going over old test results, and for whatever reason I just can't get this one into my head.

    Given the proposition

    (p \rightarrow q)\rightarrow(p \vee r \rightarrow q \vee r)

    determine whether it is a tautology
    [it is, of course], and, if it is a tautology, write the valid argument determined by it.

    In other words, figure out what rule of inference can be derived from this argument. I believe it is modus tollens, but am not sure, and just can't see what method I would use to go about this. Any ideas?

    Thanks to all the good people out there!
    Hi epicurean.

    Modus tollens is the tautology ((p\rightarrow q)\wedge\neg\,q)\rightarrow\neg\,p. I have no idea what your tautology is called.
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  3. #3
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    Abstractionist,

    Thanks for taking a look at it. Now that I look at it again, it appears to be much closer to Resolution, but still isn't quite right. Methinks it could bear more looking at from my side. Thanks again!
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