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Math Help - A rules of inference question

  1. #1
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    A rules of inference question

    This might be easy for some, but I seem to be having a bit of trouble grasping the concepts behind rules of inference.

    Given the premises “if it doesn’t snow or if the roads are clear, then I will drive to Montreal and visit my sister,” “if I drive to Montreal, I can visit a museum,” and “I do not visit a museum,” use the rules of inference to determine whether or not “It snowed” is a valid conclusion.
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  2. #2
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    Quote Originally Posted by Runty View Post
    Given the premises “if it doesn’t snow or if the roads are clear, then I will drive to Montreal and visit my sister,” “if I drive to Montreal, I can visit a museum,” and “I do not visit a museum,” use the rules of inference to determine whether or not “It snowed” is a valid conclusion.
    Forget the sister bit. It has nothing to do with question.
    \begin{array}{*{20}c}<br />
   {\left( {\neg S \vee C} \right) \to M}  \\<br />
   {M \to V}  \\<br />
   {\neg V}  \\<br />
\hline<br />
   {\neg M}  \\<br />
   {S \wedge \neg C}  \\<br />
   S  \\ \end{array}

    Now you supply reasons.
    Last edited by Plato; January 26th 2010 at 09:26 AM.
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    Quote Originally Posted by Plato View Post
    Forget the sister bit. It has nothing to do with question.
    \begin{array}{*{20}c}<br />
   {\left( {\neg S \vee C} \right) \to M}  \\<br />
   {M \to V}  \\<br />
   {\neg V}  \\<br />
\hline<br />
   {\neg M}  \\<br />
   {S \wedge \neg C}  \\<br />
   S  \\ \end{array}

    Now you supply reasons.
    That does help a bit, but I could use a bit more detail (these rules are a bit difficult to wrap my head around). Does your answer show that the conclusion is valid or invalid?
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  4. #4
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    It snowed is valid.
    We use modus tollens twice.
    Then simplification.
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