Consider the following statements: P: Good mobile phones are not cheap Q:…
2014
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.
Attempted by 147 students.
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Correct answer: D
Key insight: P and Q are contrapositives and therefore logically equivalent.
Let G mean 'a phone is good' and C mean 'a phone is cheap'.
P can be written as: G → ¬C (If a phone is good, then it is not cheap).
Q can be written as: C → ¬G (If a phone is cheap, then it is not good).
The contrapositive of P (G → ¬C) is C → ¬G, which is exactly Q. Contrapositives are logically equivalent to the original implication.
Conclusion: Since P and Q are equivalent, P implies Q, Q implies P, and P is equivalent to Q. Therefore all three statements L, M and N are true.
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