Consider the following statements: 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 one of the following about L, M, and N is CORRECT? A. Only L is TRUE. B. Only M is TRUE. C. Only N is TRUE. D. L, M and N are TRUE.

GATE 2014 · Discrete Mathematics · Propositional Logic · medium

Answer: L, M, and N are all TRUE. Answer: D.

1. Formalise P and Q symbolically: Let G = 'is good', C = 'is cheap'. P: G -> ~C (good phones are not cheap). Q: C -> ~G (cheap phones are not good). Contrapositive of P: ~(~C) -> ~G = C -> ~G = Q. So P and Q are logically equivalent.
2. Conclude truth of L, M, and N: Since P and Q are equivalent: L (P->Q) is true because equivalent statements imply each other. M (Q->P) is true for the same reason. N (P<->Q) is true because they are equivalent. All three L, M, N are TRUE.