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Math Help - Quantifiers

  1. #1
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    Quantifiers

    I am supposed to analyze a comment by film critic Robert Ebert "No good movie is long enough. No bad movie is short enough. Love Actually is good, but it is too long. I was thinking about maybe DeMorgan's Laws of Logic. Am I on the right track? Or could someone help me give me some help? Thanks...
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  2. #2
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    Re: Quantifiers

    De Morgan's law is an equivalence and is usually used as an inference rule, i.e., a way of converting one formula into another. Before you can apply De Morgan's law or any other inference rule, you need to represent the given English statements as logical formulas. For this you first need to determine your alphabet: predicate symbols, constants and possible functional symbols. This in turn depends on the structure of the English statements: what properties and objects they talk about. For example, you should decide whether you need a unary property (predicate) "_ is long", a binary property "_ lasts _ minutes" or a function "length(_)" so that you can express the fact that some film is too long or not long enough. There are also other variants to formalize the concept of movie length.
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  3. #3
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    Re: Quantifiers

    Okay. I tried to do the Quantifier part. Please let me know how this looks.

    x = good movie
    P(y) = length

    ∀x P(y) = for not every good movie, too long
    ∀x P(y) = for every good movie, not long enough

    (∃x P(y)) = there exists a movie that is good, but too long

    Thanks....
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  4. #4
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    Re: Quantifiers

    Quote Originally Posted by RatchetTheLombax View Post
    Okay. I tried to do the Quantifier part. Please let me know how this looks.
    x = good movie
    P(y) = length
    ∀x P(y) = for not every good movie, too long
    ∀x P(y) = for every good movie, not long enough
    (∃x P(y)) = there exists a movie that is good, but too long
    First, any statement "No P is Q" is symbolized as (\forall x)[P(x) \Rightarrow \neg Q(x)].

    For this we define some predicates:
    M(x) "x is a movie"; G(x) "x is good"; L(x) "x is long enough"; and S(x) "x is short enough"

    Now try it again. If these are not suitable, then redefine them to make them work.
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