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Convert sentences into First Order Logic

  1. Mar 17, 2015 #1
    (1) Anyone who is thin, tall and energetic will be good basketball player.
    (2) Some people are tall but not good basketball players.
    (3) Anyone who do exercise or eating healthy food will be energetic.
    (4) Saman is thin and tall person who do exercises.

    Write the above sentences in First Order Logic.

    I have tried like this:

    (1) ∀x thin(x) ∧ tall(x) ∧ energetic(x) → good_basketball_player(x)
    (2) ∃x tall(x) ¬ good_basketball_player(x)
    (3) ∀x do_exercise(x) ∨ eating_healthy_food(x) → energetic(x)
    (4) thin(saman) ∧ tall(saman) ∧ do_exercise(saman)
     
  2. jcsd
  3. Mar 17, 2015 #2

    TeethWhitener

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    Some parentheses in the first three sentences would help to make it clear which part the quantifiers apply to. You're also missing a ∧ in #2.
     
  4. Mar 17, 2015 #3
    Thank you. Is it correct now?

    (1) ∀x [thin(x) ∧ tall(x) ∧ energetic(x)] → good_basketball_player(x)
    (2) ∃x [tall(x) ¬ good_basketball_player(x)]
    (3) ∀x [do_exercise(x) ∨ eating_healthy_food(x)] → energetic(x)
    (4) thin(saman) ∧ tall(saman) ∧ do_exercise(saman)
     
  5. Mar 17, 2015 #4

    TeethWhitener

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    I'd probably put parentheses around the whole statement for 1 and 3. Otherwise you've got a situation where x is both a free and a bound variable.
     
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