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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?
  • a)
    Only L is TRUE
  • b)
    Only M is TRUE
  • c)
    Only N is TRUE
  • d)
    L, M and N are TRUE.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following statements:P : Good mobile phones are not cheap...
g : mobile is good
c : mobile is cheap
P : Good mobile .phones are not cheap 

Q : Cheap mobile phones are not good 

∴ Both P and Q are equivalent.

Since both P and Q are equivalent, all three of L, M, N are true.
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Most Upvoted Answer
Consider the following statements:P : Good mobile phones are not cheap...
Statement Analysis:
Let's analyze each statement one by one:

P : Good mobile phones are not cheap
This statement indicates that good mobile phones cannot be purchased at a cheap price.

Q : Cheap mobile phones are not good
This statement indicates that cheap mobile phones are not of good quality.

L : P implies Q
This statement implies that if good mobile phones are not cheap, then cheap mobile phones are not good.

M : Q implies P
This statement implies that if cheap mobile phones are not good, then good mobile phones are not cheap.

N : P is equivalent to Q
This statement implies that good mobile phones being not cheap is equivalent to cheap mobile phones not being good.

Statement Evaluation:
To evaluate the correctness of each statement, let's consider the possible scenarios:

1. If P is TRUE, then it means that good mobile phones are not cheap.
- In this case, Q (cheap mobile phones are not good) must also be TRUE because of statement L (P implies Q).
- Thus, L is TRUE.

2. If Q is TRUE, then it means that cheap mobile phones are not good.
- In this case, P (good mobile phones are not cheap) must also be TRUE because of statement M (Q implies P).
- Thus, M is TRUE.

3. If both P and Q are TRUE, then it means that good mobile phones are not cheap and cheap mobile phones are not good.
- In this case, P is equivalent to Q because both statements are TRUE.
- Thus, N is TRUE.

Conclusion:
From the analysis above, we can conclude that:
- Statement L is TRUE because if good mobile phones are not cheap, then cheap mobile phones are not good.
- Statement M is TRUE because if cheap mobile phones are not good, then good mobile phones are not cheap.
- Statement N is TRUE because good mobile phones being not cheap is equivalent to cheap mobile phones not being good.

Therefore, the correct answer is option 'D': L, M, and N are TRUE.
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Consider the following statements:P : Good mobile phones are not cheapQ : Cheap mobile phones are not goodL : P implies QM : Q implies PN : P is equivalent to QWhich one of the following about L, M and N is CORRECT?a)Only L is TRUEb)Only M is TRUEc)Only N is TRUEd)L, M and N are TRUE.Correct answer is option 'D'. Can you explain this answer?
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