Difficulty: Medium
Correct Answer: Only I follows
Explanation:
Introduction / Context:This problem tests careful handling of multiple “some” statements that may concern different individuals. A single universal inclusion (Chairs ⊆ Tables) allows one existential to propagate, but others remain unsupported.
Given Data / Assumptions:
Concept / Approach:From y ∈ Plates ∩ Chairs and Chairs ⊆ Tables, that same y is in Plates ∩ Tables, proving “Some tables are plates.” However, the existence of a bag that is a chair is not guaranteed because the “some” elements for the first two premises can be different. A universal negative like “No chair is a bag” also cannot be deduced.
Step-by-Step Solution:
I: Choose y with y ∈ Plates ∩ Chairs. Since Chairs ⊆ Tables, y ∈ Tables, hence Tables ∩ Plates ≠ ∅. I follows.II: To conclude “Some chairs are bags,” we would need a common element in Bags ∩ Chairs. But the Bag–Plate element (call it b) may differ from y; no link forces b to be a chair.III: “No chair is a bag” is a universal negative inconsistent with the possibility that b could also be a chair; since nothing forbids Bags ∩ Chairs, III is not necessary.Verification / Alternative check:Create a model with two distinct items: y is both Plate and Chair (hence also Table), and b is both Bag and Plate but not a Chair. All premises hold; I is true; II and III fail.
Why Other Options Are Wrong:Any option invoking II or III presumes connections the premises do not ensure.
Common Pitfalls:Chaining “some” statements as if they referred to the same object; assuming a universal negative without explicit support.
Final Answer:Only I follows.
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