Convert sentences into First Order Logic

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The discussion focuses on converting sentences into First Order Logic (FOL). The initial attempts included logical representations of statements regarding basketball players, exercise, and health. Participants suggested improvements, particularly emphasizing the use of parentheses for clarity in quantifier application. Corrections were made to ensure proper logical structure, including the addition of conjunctions and parentheses. The final representations aimed for accuracy in expressing the original sentences in FOL.
Upeksha
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(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)
 
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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.
 
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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)
 
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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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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