The GATE Grind

GATE 2014 CS (CS3) – Question 11

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 1 mark · Multiple choice

P: Good mobile phones are not cheap. Q: Cheap mobile phones are not good. L: P implies Q. M: Q implies P. N: P is equivalent to Q. Which is correct?

  1. Only L is true
  2. Only M is true
  3. Only N is true
  4. L, M and N are true

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Show answer and explanation

Correct answer: (D) L, M and N are true

Explanation

P is Good⇒¬Cheap. Its contrapositive is Cheap⇒¬Good, exactly Q. Thus P and Q imply each other and are equivalent. Therefore **L,M,Nalltrue,D**. Contraposition is logically valid, unlike simply reversing an implication.