The GATE Grind

GATE 2014 CS (CS3) – Question 63

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 2 marks · Multiple choice

Which formula expresses “not all rainy days are cold”?

  1. $\forall d\,(Rainy(d)\land\neg Cold(d))$
  2. $\forall d\,(\neg Rainy(d)\to Cold(d))$
  3. $\exists d\,(\neg Rainy(d)\to Cold(d))$
  4. $\exists d\,(Rainy(d)\land\neg Cold(d))$

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Show answer and explanation

Correct answer: (D) $\exists d\,(Rainy(d)\land\neg Cold(d))$

Explanation

Negate∀d(Rainy(d)⇒Cold(d)). The result is∃d(Rainy(d)∧¬Cold(d)), **D**. It asserts at least one rainy noncold day, without requiring every rainy day to be noncold.