Which of the following statements are so related that they cannot both be…
2023
Which of the following statements are so related that they cannot both be false, though they can both be true?
A. Some saints are materialists.
B. All saints are materialists.
C. No saints are materialists.
D. Some saints are not materialists.
Choose the correct answer from the options given below:
Answer: B. A and D only — CONCEPTCategorical propositions are classified as A (universal affirmative), E (universal negative), I (particular affirmative), and O (particular negative).…
- A.
A and C only
- B.
A and D only
- C.
C and D only
- D.
B and D only
Show answer & explanation
Correct answer: B
CONCEPT
Categorical propositions are classified as A (universal affirmative), E (universal negative), I (particular affirmative), and O (particular negative).
In the traditional square of opposition, I and O are subcontraries: they may both be true, but they cannot both be false, assuming the subject class has members.
APPLICATION
Classify each proposition by its quantifier and quality:
Proposition | Form | Logical role |
|---|---|---|
Some saints are materialists. | I | Particular affirmative |
All saints are materialists. | A | Universal affirmative |
No saints are materialists. | E | Universal negative |
Some saints are not materialists. | O | Particular negative |
The required relation is therefore between the I proposition and the O proposition.
CONTRAST
“Some saints are materialists” with “No saints are materialists” is the I–E contradictory pair.
“No saints are materialists” with “Some saints are not materialists” is an E–O subaltern pair.
“All saints are materialists” with “Some saints are not materialists” is the A–O contradictory pair.
RESULT
Therefore, the required pair is “Some saints are materialists” and “Some saints are not materialists”, represented in the options as A and D only.