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.

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.