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.
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AOnly I follows
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BOnly II follows
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CNeither I nor II follows
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DBoth I and II follow
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ENone of these
Answer
Correct Answer: Only II follows
Explanation
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.