Which of the following statements are so related that if one of them is true,…
2023
Which of the following statements are so related that if one of them is true, the other must be false, even though both of them can be false?
A. Some adults are far-sighted
B. No adults are far-sighted
C. All adults are far-sighted
D. Some adults are not far-sighted
Choose the correct answer from the options given below:
Answer: D. B and C only — ConceptIn the traditional square of opposition, categorical propositions are classified as universal affirmative (A), universal negative (E), particular…
- A.
A and D only
- B.
C and D only
- C.
A and B only
- D.
B and C only
Show answer & explanation
Correct answer: D
Concept
In the traditional square of opposition, categorical propositions are classified as universal affirmative (A), universal negative (E), particular affirmative (I), and particular negative (O). Contrary propositions cannot both be true, but they can both be false.
Application
Some adults are far-sighted is a particular affirmative (I) proposition.
No adults are far-sighted is a universal negative (E) proposition.
All adults are far-sighted is a universal affirmative (A) proposition.
Some adults are not far-sighted is a particular negative (O) proposition.
The contrary pair is the universal affirmative and the universal negative: All adults are far-sighted and No adults are far-sighted.
Cross-check
If some adults are far-sighted and some are not, both universal statements are false. This confirms that the two universal statements can both be false, while they cannot both be true.
Therefore, the answer is B and C only.