In the traditional square of opposition, which pair of the following…
2025
In the traditional square of opposition, which pair of the following categorical statements cannot both be false, although they can both be true?
A. All cows are bovines.
B. Some cows are bovines.
C. Some cows are not bovines.
D. No cows are bovines.
Choose the correct answer from the options given below.
Answer: C. B and C Only — ConceptThe traditional square of opposition classifies categorical propositions as A (universal affirmative), E (universal negative), I (particular…
- A.
A and C Only
- B.
B and D Only
- C.
B and C Only
- D.
C and D Only
Show answer & explanation
Correct answer: C
Concept
The traditional square of opposition classifies categorical propositions as A (universal affirmative), E (universal negative), I (particular affirmative), and O (particular negative). Under its existential-import convention, I and O are subcontraries: they may both be true, but they cannot both be false.
Application
Classify the four statements: A is an A-proposition, B is an I-proposition, C is an O-proposition, and D is an E-proposition.
Statement
Form
Classification
A
A
Universal affirmative
B
I
Particular affirmative
C
O
Particular negative
D
E
Universal negative
The condition in the question is precisely the subcontrary relation.
Statements B and C instantiate the I-O pair, so they have the required relation.
Cross-check and contrast
A and C form the A-O contradictory pair; contradictories cannot both be true and cannot both be false.
B and D form the I-E contradictory pair; they also cannot both be true or both be false.
C and D lie on the O-E negative subalternation line; this is not the subcontrary relation described in the stem.
Result
Therefore, the required pair is B and C only.