Intersecting particulars problem: given ‘‘Some books are tables’’ and ‘‘Some tables are mirrors’’ decide whether mirrors overlap books or whether books and mirrors are disjoint.

Question

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

Curioustab · Accepted Answer

Both premises are particular and speak only about overlaps with Tables.Premise 1: Books ∩ Tables ≠ ∅.Premise 2: Tables ∩ Mirrors ≠ ∅.Conclusions: I. Some mirrors are books. II. No book is mirror.Concept/ApproachTwo separate overlaps with the same middle set do not force a direct overlap, nor do they preclude it. Both a positive and a negative relation between Books and Mirrors remain possible.Testing conclusion IThere need not be a common element across all three sets. The book table items and the table mirror items could be different elements. Hence I is not necessary.Testing conclusion IIThe premises do not rule out Books ∩ Mirrors. Therefore claiming disjointness is not justified; II does not follow.Verification/AlternativeModel A: Tables = {x, y}, Books = {x}, Mirrors = {y} gives neither overlap nor disjoint proof of I or II. Model B: Tables = {x}, Books = {x}, Mirrors = {x} makes I true and II false. Since both patterns are possible, neither conclusion is forced.Common pitfallsAssuming transitivity for particular statements with the same middle term.Final AnswerNeither I nor II follows.

Intersecting particulars problem: given ‘‘Some books are tables’’ and ‘‘Some tables are mirrors’’ decide whether mirrors overlap books or whether books and mirrors are disjoint.

Answer

Explanation