Statements: • All poets are day dreamers. • All painters are day dreamers. Conclusions: I. All painters are poets. II. Some day dreamers are not painters. Choose the option that must follow.

Introduction / Context:
This problem features two universal subset claims into the same superset and asks for necessary relations between the two subsets and the complement region. Without extra premises, neither a subset inclusion between Painters and Poets nor guaranteed existence outside Painters can be asserted.

Given Data / Assumptions:

• Poets ⊆ DayDreamers.
• Painters ⊆ DayDreamers.
• No statement about overlaps or existence beyond these inclusions.

Concept / Approach:
From two subsets contained in the same superset, nothing follows about the relation between the subsets unless additional information is provided. Also, conclusions that assert existence (“some … are not …”) require explicit or deducible witnesses.

Step-by-Step Solution:
1) Conclusion I (“All painters are poets”) would require Painters ⊆ Poets, which is not given; both could be disjoint or overlapping within DayDreamers.2) Conclusion II (“Some day dreamers are not painters”) is not guaranteed. It might be that all day dreamers are painters, or that there exist non-painter day dreamers; both models satisfy the premises.

Verification / Alternative check:
Model A: DayDreamers = Painters (and Poets empty). Premises hold; Conclusion II fails. Model B: DayDreamers = Poets (and Painters empty). Premises hold; Conclusion II again fails. Therefore II is not necessary. Model C: DayDreamers includes many non-painters; here II would be true, showing it is contingent, not necessary.

Why Other Options Are Wrong:
Options asserting I or II assume information not present in the premises.

Common Pitfalls:
Inferring relations between two subsets just because they share a superset, and assuming existence of elements outside a subset without an existential claim.

Final Answer:
Neither I nor II follows.