Syllogism — Distinguish converses from valid consequences Statements: • All plastics are glasses. • Some sponges are glasses. • All sponges are clothes. • All clothes are liquids. Conclusions: I) All liquids are sponges. II) Some plastics are clothes. III) All glasses are plastics. IV) All liquids are clothes. Choose the correct evaluation.

Introduction / Context:
This item is designed to expose two common errors: (1) inferring converses (e.g., from A ⊆ B to B ⊆ A), and (2) forcing intersections without evidence. We must test each conclusion strictly against the premises.

Given Data / Assumptions:

• Plastics ⊆ Glasses.
• ∃x: x ∈ Sponges ∩ Glasses.
• Sponges ⊆ Clothes.
• Clothes ⊆ Liquids.

Concept / Approach:
Conclusions that reverse an inclusion (e.g., “All glasses are plastics”) are invalid. Claims that everything in a larger set must be inside a smaller subset (“All liquids are sponges”) also fail absent explicit premises. Finally, while Clothes ⊆ Liquids is true, the converse “All liquids are clothes” is not supported.

Step-by-Step Solution:

Verification / Alternative check:
Model: Let Plastics be a tiny subset of Glasses, Sponges a separate subset of Glasses, Clothes a large set contained in Liquids, and Liquids much larger. All premises hold; none of I–IV must be true.

Why Other Options Are Wrong:
Options claiming II and/or IV rely on unjustified overlaps or converses.

Common Pitfalls:
Converse errors and assuming that if a subset lies inside a superset, then the superset collapses back into the subset.

Final Answer:
None follows.