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The CORRECT formula for the sentence, "not all rainy days are cold" is

1. ∀d (Rainy(d) ∧ ~Cold(d))
2. ∀d (~Rainy(d) → Cold(d))
3. ∃d (~Rainy(d) → Cold(d))
4. ∃d (Rainy(d) ∧ ~Cold(d))

Correct answer: ∃d (Rainy(d) ∧ ~Cold(d))

Solution

The correct option indicates that there exists at least one day that is rainy and not cold, which accurately reflects the meaning of the original sentence that not all rainy days are cold.

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