Syllogism — From the premises below, select the conclusion(s) that must hold: Statements: • Some bags are pockets. • No pocket is a pouch. Conclusions: I. Some bags are not pouches. II. Some pockets are bags.

Introduction / Context:
This item pairs an existential overlap with a universal negative about one of the sets. The question is designed so that both directions of the “some” intersection can be affirmed and a negative conclusion is forced for at least some bags.

Given Data / Assumptions:

• S1: Some Bags are Pockets (Bags ∩ Pockets ≠ ∅).
• S2: No Pocket is a Pouch (Pockets ∩ Pouches = ∅).
• Conclusions: I “Some Bags are not Pouches.” II “Some Pockets are Bags.”

Concept / Approach:
From S1, take an element that is both Bag and Pocket. S2 then guarantees that element is not a Pouch. That single witness proves I. S1 also directly implies II because “Some Bags are Pockets” is symmetric as an intersection statement: there exist Pockets that are Bags.

Step-by-Step Solution:
1) Pick x with Bag(x) and Pocket(x) (by S1).2) From S2, Pocket(x) ⇒ not Pouch(x).3) Therefore Bag(x) and not Pouch(x) ⇒ “Some Bags are not Pouches” (I) holds.4) Because x is also a Pocket, “Some Pockets are Bags” (II) is witnessed by the same element.

Verification / Alternative check:
Venn diagram: Bags and Pockets overlap; Pockets and Pouches are disjoint. The overlap region is necessarily outside Pouches, establishing I, and symmetry of overlap confirms II.

Why Other Options Are Wrong:
Choices that keep only one conclusion ignore the dual implications from the same witness; “neither” contradicts the guaranteed overlap.

Common Pitfalls:
Missing that “some A are B” automatically implies “some B are A,” and overlooking how a universal negative eliminates membership in a third set.

Final Answer:
Both Conclusion I and Conclusion II follow.