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Inference Rule with Quantifier and implication

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data
    All healthy food does not taste good. "
    Spinach is a healthy food. Duncan only want to eat tasty food. Duncan does not eat spinach. Hamburger is not a healthy food.

    Write all possible conclusion.
    I try to translate it into proposition with quantifier, such as [tex]t(x)=[/tex]x is tasty, [tex]h(x)=[/tex]x is healthy, [tex]d(x)=[/tex] Doddy eats x.

    3. The attempt at a solution

    I think [tex]d(hamburger)[/tex] is not a conclusion because the argument is [tex]d(x) \rightarrow t(x)[/tex]. We cannot conclude [tex]d(hamburger)[/tex] or [tex]t(hamburger)[/tex], because proposition said [tex]h(x) \rightarrow ~t(x)[/tex] and [tex]d(x) \rightarrow t(x)[/tex]. Is it right?
     
  2. jcsd
  3. Oct 15, 2008 #2

    HallsofIvy

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    Yes, that is correct. (Assuming that "Doddy" is a nickname for "Duncan"!) Saying "All healthy food does not taste good" does NOT imply that unhealthy food does taste good. Of course, "not d(spinach)" would be a conclusion from the first two statements but that is given as the third statement.
     
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