Which pair of statements is related in such a way that the two statements can…
2024
Which pair of statements is related in such a way that the two statements can neither both be true nor both be false?
Statement | Proposition |
|---|---|
A | All dogs are omnivores. |
B | Some dogs are omnivores. |
C | Some dogs are not omnivores. |
D | No dogs are omnivores. |
Choose the correct answer from the options given below.
Answer: A. A and C only — ConceptIn the traditional square of opposition, a contradictory pair consists of two propositions that cannot both be true and cannot both be false. Exactly…
- A.
A and C only
- B.
B and C only
- C.
C and D only
- D.
A and D only
Show answer & explanation
Correct answer: A
Concept
In the traditional square of opposition, a contradictory pair consists of two propositions that cannot both be true and cannot both be false. Exactly one member of the pair must be true.
The four categorical forms are A: universal affirmative (All S are P), E: universal negative (No S are P), I: particular affirmative (Some S are P), and O: particular negative (Some S are not P). The contradictory diagonals are A–O and E–I.
Form | Quantity and quality | Pattern |
|---|---|---|
A | Universal affirmative | All S are P |
E | Universal negative | No S are P |
I | Particular affirmative | Some S are P |
O | Particular negative | Some S are not P |
Application
Statement A, ‘All dogs are omnivores,’ has the A form: universal affirmative.
Statement C, ‘Some dogs are not omnivores,’ has the O form: particular negative.
A and C therefore instantiate the A–O diagonal. If A is true, C is false; if A is false, C is true.
Cross-check and contrast
B and C are the I–O subcontrary pair; they may both be true.
C and D are the O–E subalternation pair, not a contradictory diagonal.
A and D are the A–E contrary pair; they cannot both be true but may both be false.
Result
Therefore, the required pair is A and C only.