The CORRECT formula for the sentence, “not all rainy days are cold” is
(A) A
(B) B
(C) C
(D) D
Answer: (D)
Explanation: (A) Note that (p ∧ ~q) ≡ ~(p -> q). So it means rainy day to cold implication is false for all days. Which means non-rainy days are cold.
(B) For all days, if day is not rainy, then it is cold [Non-Rainy days are cold]
(C) There exist some days for which not rainy implies cold. [Some non-rainy days are cold]
(D) Note that (p ∧ ~q) ≡ ~(p -> q). So it means rainy day to cold implication is false for some days. Which means not all rainy days are cold.