Statements: • Some days are nights. • Some nights are weeks. • Some weeks are months. • All months are years. Conclusions: I. Some years are nights. II. Some years are days. III. Some months are nights. IV. Some years are weeks. Choose the option that must follow.

Introduction / Context:
This chain contains several “some” links and one universal inclusion. Only statements that depend solely on the universal step and an existential that directly feeds it can be guaranteed.

Given Data / Assumptions:

• ∃w_m ∈ Weeks ∩ Months.
• All Months ⊆ Years.
• Also, ∃d_n ∈ Days ∩ Nights and ∃n_w ∈ Nights ∩ Weeks (not guaranteed to be the same as w_m).

Concept / Approach:
If some Weeks are Months and all Months are Years, then those particular Weeks are also Years. This alone forces “Some Years are Weeks.” Any attempt to link Nights or Days to Years would require the very same individuals to traverse multiple “some” links, which is not compelled.

Step-by-Step Solution:
1) From “Some Weeks are Months,” choose w_m ∈ Weeks ∩ Months.2) From “All Months are Years,” w_m ∈ Years, hence Years ∩ Weeks ≠ ∅ → IV holds.3) For I and III, we would need an element that is both Night and Month (or Year). The premises do not ensure this.4) For II, nothing connects the given Day to Month or Year.

Verification / Alternative check:
Build a model where the Night–Week witness is different from the Week–Month witness. Then IV is still true, but I–III are undetermined.

Why Other Options Are Wrong:
They assume unintended identity across separate existential statements.

Common Pitfalls:
Chaining “some” statements as if they were universal.

Final Answer:
Only IV follows.