3

Could someone explain why the following sentence:

“Some lions do not drink coffee.”

is not translated to ∃x(P (x) → ¬R(x))

Thank you!

6

Implication (→) is rarely used with the existential quantifier when translating from natural language, so beware of that.

Your formulation is wrong because if there are no lions it comes out true, since the antecedent of the conditional would be false for every x.

"Some lions do not drink coffee" is translated with conjunction instead, as:

∃x(P(x) ∧ ¬R(x))

since the sentence asserts that there are (at least one) things that are both lions and not coffee drinkers.

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