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Math Help - converting words into logic symbols

  1. #1
    Member Jskid's Avatar
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    converting words into logic symbols

    To run a marathon you must be over 5 feet and have a healthy heart. If you are not over 5 feet and do not have a healthy heart, you cannot run the marathon. Right this statement in symbols.

    Let a(x) be the assertion "x can run the marathon"
    For the first statement I got (over 5 feet) \wedge (healthy heart) \rightarrow a(x)
    For the second statement I got \neg (over 5 feet) \wedge \neg (healthy heart) \rightarrow \neg a(x)

    I have a feeling this is wrong because if the hypothesis is false then the statment is true, if I don't use implication what do I use?
    Last edited by Jskid; September 20th 2011 at 06:16 PM. Reason: changed latex
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  2. #2
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    Re: converting words into logic symbols

    The first formula should be \forall x\,(\mathop{\mbox{over 5 feet}}(x) \wedge \mathop{\mbox{healthy heart}}(x)\rightarrow a(x)), and similarly for the second.

    The use of implication is correct. These statements are true for all x, including those for whom the premises are false.
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  3. #3
    Member Jskid's Avatar
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    Re: converting words into logic symbols

    Quote Originally Posted by emakarov View Post
    The first formula should be \forall x\,(\mathop{\mbox{over 5 feet}}(x) \wedge \mathop{\mbox{healthy heart}}(x)\rightarrow a(x)), and similarly for the second.

    The use of implication is correct. These statements are true for all x, including those for whom the premises are false.
    What does "premises" mean? Is that an synonym for hypothesis?
    Last edited by Jskid; September 21st 2011 at 01:00 PM. Reason: changed acronym to synonym
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  4. #4
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    Re: converting words into logic symbols

    Yes, a synonym. It's what is located left of the arrow.
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