Syllogism — Mix of “some” overlaps and a universal inclusion Statements: • Some bags are plates. • Some plates are chairs. • All chairs are tables. Conclusions: I) Some tables are plates. II) Some chairs are bags. III) No chair is a bag. Identify what necessarily follows.

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:

• ∃x: x ∈ Bags ∩ Plates.
• ∃y: y ∈ Plates ∩ Chairs.
• Chairs ⊆ Tables.

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:

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.