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Math Help - prove by rules of inference

  1. #1
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    prove by rules of inference

    I have premises
    (1) p
    (2) p\rightarrow q
    (3) r
    and conclusion
    ( p\vee q)  \rightarrow r

    I've checked that the argument is valid.
    But I still cannot find a way to show it by using rules of inference.
    please...
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  2. #2
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    Re: prove by rules of inference

    Which exactly system of inference rules are you using? See this sticky thread.
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  3. #3
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    Re: prove by rules of inference

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  4. #4
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    Re: prove by rules of inference

    Quote Originally Posted by deniselim17 View Post
    I have premises
    (1) p
    (2) p\rightarrow q
    (3) r
    and conclusion
    ( p\vee q)  \rightarrow
    From (3) we get \neg \left( {p \vee q} \right) \vee r by addition.

    Then by material implication we get \left( {p \vee q} \right) \to r.
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  5. #5
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    Re: prove by rules of inference

    Another way is to have p\lor q\vdash r just because r is a premise and use the Deduction theorem (or Conditional Introduction).
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  6. #6
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    Re: prove by rules of inference

    So, premise (1) and premise (2) are not really necessary here?
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  7. #7
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    Re: prove by rules of inference

    That's right.
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