1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Inference Rule with Quantifier and implication
  1. Bayesian inference (Replies: 6)

  2. Rules of implication (Replies: 2)