Define the following predicates as:

F(x): x is a footballer

C(x): x is a football club

P(x,y): x plays for y

Consider the following sentence of FOL: ∃x(F(x) ∧ ∀y(C(y) → P(x,y)))

Is the translation from FOL into English the following: "There is a footballer playing at every football club"?


Your translation is potentially correct but ambiguous in English, it could mean that every football club has at least one player. A better translation is "there exists a footballer who plays for every club."

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