Categorical logic with a universal negative and a universal affirmative: from ‘‘No magazine is cap’’ and ‘‘All caps are cameras’’ decide whether any statement about cameras and magazines is compelled.

Question

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

Curioustab · Accepted Answer

Translate and inspect the relations. Premise 1: No magazine is a cap, so Magazines ∩ Caps = ∅. Premise 2: All caps are cameras, so Caps ⊆ Cameras. Conclusions: I. No camera is magazine. II. Some cameras are magazines. Concept/ApproachOnly the cap portion of Cameras is known to be disjoint from Magazines. Cameras outside Caps could still overlap with Magazines; or they might not.Testing conclusion II claims Cameras ∩ Magazines = ∅ which is stronger than the premises. Not forced, so I does not follow.Testing conclusion IIII claims Cameras ∩ Magazines ≠ ∅ which is also not forced. Therefore II does not follow.Verification/AlternativeTwo models show independence: (a) Cameras = Caps, Magazines disjoint from all Cameras makes I true, II false. (b) Cameras include a non cap region that overlaps Magazines makes II true, I false. Since both are possible, neither conclusion is necessary.Common pitfallsOverextending properties of a subset to the entire superset.Final AnswerNeither I nor II follows.