Syllogism — Shoes, White, and Blue: Statements: (a) Some shoes are White. (b) All White are Blue. Conclusions to test: I. All shoes are Blue. II. Some shoes are Blue.

Introduction / Context:We must propagate a particular statement through a universal inclusion and see what minimum conclusion is guaranteed.

Given Data / Assumptions:

• Some shoes are White (∃ Shoe ∩ White).
• All White are Blue (White ⊆ Blue).

Concept / Approach:A subset mapping carries the “some” individuals along: the shoes that are White are necessarily Blue. But this does not make all shoes Blue.

Step-by-Step Solution:1) Take the shoes that are White (exist by premise).2) Since White ⊆ Blue, those shoes are Blue.3) Therefore, “Some shoes are Blue” follows, while “All shoes are Blue” does not.

Verification / Alternative check:Construct a model with many non-White shoes; I is false but II remains true.

Why Other Options Are Wrong:(a) overgeneralizes; (c) and (d) misjudge necessity.

Common Pitfalls:Confusing “some” with “all.”

Final Answer:Only II follows.