Work each conclusion directly from the premises.
- Premise 1: Some desks are caps, so Desks ∩ Caps ≠ ∅.
- Premise 2: No cap is red, so Caps ∩ Red = ∅.
- Conclusions: I. Some caps are desks. II. No desk is red.
Concept/ApproachParticular statements convert, while universal negatives do not automatically extend to supersets.Testing conclusion IFrom Some desks are caps we can convert to Some caps are desks. Hence I follows.Testing conclusion IIOnly caps are known to be non red. Desks that are not caps might still be red. Thus II is not guaranteed.Verification/AlternativeModel: Caps = {a}, Desks = {a, d2}, Red = {d2}. Premises hold; I true, II false.Common pitfallsExtending a restriction on a subset to the entire superset.Final AnswerOnly conclusion I follows.
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