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+25 votes

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?

  1. Only L is TRUE.
  2. Only M is TRUE.
  3. Only N is TRUE.
  4. L, M and N are TRUE.
asked in Mathematical Logic by Veteran (96.2k points)
edited by | 2.3k views

2 Answers

+41 votes
Best answer

Correct Answer (D)

Lets break the given compound statements into atomic statements.

  • A : Good mobile phones.
  • B : Cheap mobile phones.

$P :(A\to \neg B) \iff (\neg A\vee \neg B)$
$Q :(B\to \neg A) \iff \big((\neg B\vee \neg A) \iff \neg A\vee \neg B)\big)$ (Disjunction is commutative),
Hence, $(P\iff Q)$ which means $(P\to Q)$ and $(Q \to P).$

answered by Active (3.8k points)
edited by
Nice Explanation

@Arjun sir

Please explain

How to break this statement  into conditional statement ??

  • P: Good mobile phones are not cheap
  • Q: Cheap mobile phones are not good

This might help ....

Crystal clear....thqqq
P and Q are contrapositives of each other.
+3 votes
P and Q are contra-positives to each other. A proposition and its contra-positive are always equivalent.

Equivalent and <--> are same, so p <--> q holds.

So option D)
answered by Loyal (7.4k points)
can you please explain me the line "P is equivalent to Q, which means P implies Q ,and Q implies P" .

P implies Q means P->Q  and Q implies P means Q->P then how can we conclude these two from the fact that P is equivalent to Q.
P is equivalent to Q means (P->Q)^(Q->P). So both (P->Q) and (Q->P) must be true to ensure this.

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