Syllogism – Test for unwarranted intersection: Statements: 1) All apples are oranges. 2) Some oranges are papayas. Conclusions: I) Some apples are papayas. II) Some papayas are apples. Choose which conclusions must follow.
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AOnly Conclusion II follows
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BBoth Conclusions I and II follow
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CNeither Conclusion I nor II follows
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DOnly Conclusion I follows
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ENone of these
Answer
Correct Answer: Neither Conclusion I nor II follows
Explanation
Introduction / Context:This item checks whether you incorrectly assume overlap between Apples and the specific Oranges that are Papayas.
Given Data / Assumptions:
- All Apples ⊆ Oranges.
- Some Oranges are Papayas (∃ O∩P).
Concept / Approach:“Some O are P” does not guarantee that those O are the apples. Without a premise tying Apples to Papayas, no Apple–Papaya intersection is necessary.
Step-by-Step Solution:C1: Some apples are papayas – not forced; the papaya-oranges might be non-apple oranges.C2: Some papayas are apples – the converse is equally unforced.
Verification / Alternative check:Model with Apples as a small subset of Oranges and pick Papayas among Oranges disjoint from Apples. Premises hold; both conclusions fail.
Why Other Options Are Wrong:Any option claiming one or both conclusions follow contradicts the countermodel above.
Common Pitfalls:Assuming that a subset (Apples) must share the incidental overlap of its superset (Oranges) with a third set (Papayas).
Final Answer:Neither Conclusion I nor II follows.