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 true, nor can they both be false?
A. All mammals are vertebrates.
B. Some mammals are vertebrates.
C. Some mammals are not vertebrates.
D. No mammals are vertebrates.
Choose the correct answer from the options given below:
Answer: B. B and D 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 D only
- C.
C and D only
- D.
A and D only
Show answer & explanation
Correct answer: B
CONCEPT
In the traditional square of opposition, categorical propositions are classified by quantity (universal or particular) and quality (affirmative or negative). Contradictories differ in both quantity and quality.
For the same subject and predicate, an A-form contradicts an O-form, and an E-form contradicts an I-form. Contradictories cannot both be true and cannot both be false.
APPLICATION
“All mammals are vertebrates” is a universal affirmative proposition, the A-form.
“Some mammals are vertebrates” is a particular affirmative proposition, the I-form.
“Some mammals are not vertebrates” is a particular negative proposition, the O-form.
“No mammals are vertebrates” is a universal negative proposition, the E-form.
The contradictory pairs are A–O and E–I. Among the offered pairs, “Some mammals are vertebrates” and “No mammals are vertebrates” form the E–I pair.
CONTRAST
“A and B only” combines A and I: both are affirmative, so they are related by subalternation rather than contradiction.
“C and D only” combines O and E: both are negative, so they are related by subalternation rather than contradiction.
“A and D only” combines A and E: both are universal; they are contraries and may both be false.
Therefore, the required pair is “B and D only”.