Particular conversion and scope of a universal negative: from ‘‘Some desks are caps’’ and ‘‘No cap is red’’ decide which conclusions about caps being desks and desks being non red are compelled.

Question

Solve this multiple-choice question and choose the correct option.

Curioustab · Accepted Answer

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.