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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.
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5 Answers

Best answer
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72 votes

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 $(Q \to P).$

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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)
1 votes
1 votes
P: Good mobile phones are not cheap (False: some good mobile phones are cheap)

Q: Cheap mobiles are not good ( False: some cheap phones are also good)

L: P→Q : False → False : True

M: Q→P: False → False: True

N: P=Q: True

Hence L,M,N are True ans is (D)

 

Please correct me if my approach is wrong.
Answer:

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