The correct answer is: A and C Only.
Key Points
The question deals with the logical relationship between propositions. Propositions may be related as contradictory, contrary, sub-contrary, or sub-altern depending on their logical structure. When two propositions are such that both cannot be true at the same time but both can be false, they are known as contrary propositions. In categorical logic, universal affirmative (A-type) and universal negative (E-type) propositions form a pair of contraries. This understanding helps identify which options fit the condition of “if one is true, the other must be false, although both can be false.”
- Analysis of the Propositions:
- A. “All novels are books.” – This is a Universal Affirmative (A-type) statement.
- C. “No novels are books.” – This is a Universal Negative (E-type) statement.
- B. “Some novels are not books.” – This is a Particular Negative (O-type).
- D. “Some novels are books.” – This is a Particular Affirmative (I-type).
Among these, the A-type (All novels are books) and E-type (No novels are books) are contraries. Their relationship fits the exact condition given:
- If A is true, C must be false.
- If C is true, A must be false.
- But both A and C can be false at the same time (e.g., some novels are books, some are not).
Therefore, the pair that satisfies the given condition is A and C only.
Additional Information
- Universal Affirmative (A-type) — “All S are P”
- This type asserts that every member of the subject class is included in the predicate class.
- Example: “All birds are animals.”
- It contradicts O-type and is contrary to E-type.
- Universal Negative (E-type) — “No S are P”
- Asserts that no member of the subject class belongs to the predicate class.
- Example: “No fishes are mammals.”
- It contradicts I-type and is contrary to A-type.
- Contrary Propositions:
- Both cannot be true simultaneously.
- Both can be false at the same time.
- Pairs: A-type and E-type only.
- Application to This Question:
- “All novels are books” (Universal Affirmative) and “No novels are books” (Universal Negative) fall into this category.
- Therefore, they are contrary propositions as per classical logic.