Which of the following statements are so related that if one of them is false,…
2023
Which of the following statements are so related that if one of them is false, the other must be true, even though both of them can be true?
A. Some cars are e-vehicles.
B. Some cars are not e-vehicles.
C. No cars are e-vehicles.
D. All cars are e-vehicles.
Choose the correct answer from the options given below:
Answer: A. A and B only — ConceptIn the traditional square of opposition, categorical propositions are classified by quantity (universal or particular) and quality (affirmative or…
- A.
A and B only
- B.
B and C only
- C.
A and C only
- D.
C and D only
Show answer & explanation
Correct answer: A
Concept
In the traditional square of opposition, categorical propositions are classified by quantity (universal or particular) and quality (affirmative or negative). A and E propositions are universal; I and O propositions are particular.
Subcontraries are the two particular propositions I and O: they cannot both be false, although they may both be true. Contradictories cannot both be true or both be false, while contraries cannot both be true.
Application
Statement A, “Some cars are e-vehicles,” is an I proposition: particular affirmative.
Statement B, “Some cars are not e-vehicles,” is an O proposition: particular negative.
Because A and B are the I–O pair, they are subcontraries: if either is false, the other must be true, and both can be true when some cars are e-vehicles and some are not.
Thus the required pair is A and B.
Contrast
B and C are O and E propositions of the same negative quality; this is subalternation, not subcontrariety.
A and C are I and E propositions; they are contradictories, so they cannot both be true and cannot both be false.
C and D are E and A propositions; they are contraries, so they cannot both be true, although both may be false.
Result
The correct answer is A and B only.