Statements: • Some drums are posters. • All posters are windows. • Some windows are tablets. • All tablets are books. Conclusions: I. Some windows are drums. II. Some books are posters. III. Some tablets are drums. Choose the option that must follow.

Introduction / Context:A universal inclusion pushes an existential backward to establish one guaranteed overlap. Other proposed overlaps require identity across independent “some” claims, which is not imposed by the premises.

Given Data / Assumptions:

• ∃d_p ∈ Drums ∩ Posters.
• Posters ⊆ Windows.
• ∃w_t ∈ Windows ∩ Tablets.
• Tablets ⊆ Books.

Concept / Approach:From d_p ∈ Posters and Posters ⊆ Windows, it follows that Windows ∩ Drums ≠ ∅ (I true). II would require Posters to reach Books via Tablets; not forced. III would need the Windows that are Tablets to coincide with the Windows that are Posters∩Drums; again, not forced.

Step-by-Step Solution:• I: Direct consequence of the universal inclusion.• II: Needs some Poster to be a Tablet; not stated.• III: Needs the Tablet-window to be the Poster-window-drum; not stated.

Verification / Alternative check:Choose disjoint witnesses for Windows∩Tablets and Drums∩Posters; then only I holds.

Why Other Options Are Wrong:They add non-forced identities across different “some” statements.

Common Pitfalls:Assuming all given windows are the same items.

Final Answer:Only I follows.