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Math Help - Predicate Logic

  1. #1
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    Predicate Logic

    I had Discrete math in my undergrad CompSci program, I am now in grad school and having to use it again and I am a bit rusty: Need help with verifying some predicate logic translations.

    English: Notevery airport has a runway for large jets.
    My translation:
    hasrunwayfor(x,j,l): true if airport x has a runway for jet j, that is large l, false otherwise
    My Formula: ∃x:Airport|∀j:Jet|Runway(j,l)
    Do my translation and formula look correct?
    Help is greatly appreciated. Thanks in advance
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  2. #2
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    Quote Originally Posted by jds80021 View Post
    English: [FONT=&quot]Notevery airport has a runway for large jets.
    This may be a surprise, but that statement is logically equivalent to:
    Some airport does not have a runway for large jets.
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  3. #3
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    Plato,
    is it possible to use a conjunction in this case. Such as:
    <br />
(\forall A)(\exists R_{Large})[A \wedge \neg R_{Large}]<br />

    Although this would be true for airports without large runways - something different.
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  4. #4
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    Logical equivalent

    Thanks Plato, Yes, I can see the logical equivalent , but what is the predicate logic statement and formula?
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  5. #5
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    Quote Originally Posted by bmp05 View Post
    Plato,
    is it possible to use a conjunction in this case. Such as:
    <br />
(\forall A)(\exists R_{Large})[A \wedge \neg R_{Large}]<br />

    Although this would be true for airports without large runways - something different.
    <br />
(\forall A)(\exists R_{Large})[A \wedge \neg R_{Large}]<br />
    That tranlates as "All airports have a runway not for large jets."
    Is that logically equivalent to “Not every airport has a runway for large jets.”?
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  6. #6
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    Plato. There should be a computer program for this- and there is isn't there? Prolog or something?

    Anyway, I was way off the mark... so what about: "Some airports have a runway not for large jets?"
    (\exists A)(\forall R_{Large})[A \wedge \neg R_{Large}]

    Runway(A, B) can this type of statement (?) always be replaced by a simpler statement?
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  7. #7
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    If L(x) is the predicate “x has a runway for large jets” and
    A(x) is the predicate “x is an airport”.
    Then the translation is \left( {\exists x} \right)\left[ {A(x) \wedge \neg L(x)} \right] .
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