[Math] Translating an English sentence into predicate logic

logic-translationpredicate-logic

I have a question where I was given the following atomic propositions:

Let H(x) = x can ski

Let P(x) = x plays soccer

Note: The universe of discourse is all humans

I was tasked to translate the following sentence logically:

No one who can ski plays soccer

I came up with two solutions for this sentence and I'm unsure if one is considered more correct:

  1. ∀x(¬(P(x)∧H(x))

  2. ∀x (H(x) -> ~p(x))

Symbols Reference

Best Answer

Your second sentence can be rescued by removing the negation at the beginning: $$\forall x (H(x)\to\neg P(x)).$$ This translates to, For every person, if they ski, they don't play soccer. This is equivalent in English to saying that nobody who skis plays soccer.

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