Logical syllogism — test what necessarily follows from “some” statements Statements: • Some tapes are discs. • Some discs are cassettes. • Some cassettes are songs. Conclusions to evaluate: I. Some songs are discs. II. Some cassettes are tapes. III.

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

Accepted Answer

Introduction / Context:This verbal reasoning problem checks your command of categorical logic with “some” statements. When premises use qualifiers like some, you must be careful not to over infer intersections that are not guaranteed. The task is to decide which, if any, of the proposed conclusions must be true based only on the given statements. Given Data / Assumptions: Some tapes are discs. Some discs are cassettes. Some cassettes are songs. No information is given about universal inclusion (all) or exclusions (no) among these four sets beyond the three some relations. Concept / Approach:In set logic, “some A are B” only asserts a nonempty overlap between A and B. Two separate some statements that share a middle term (for example tapes–discs and discs–cassettes) do not force an overlap between the outer classes (tapes and cassettes). Chains of some statements cannot be freely transitive without extra data. A conclusion follows only if it holds in every model consistent with the premises. Step-by-Step Solution: Test I (Some songs are discs): You can construct a model where the cassettes that are songs are disjoint from the discs that overlap tapes. Therefore I is not necessary.Test II (Some cassettes are tapes): From some tapes–discs and some discs–cassettes, the overlap could be with different parts of discs. Thus tapes and cassettes may still be disjoint. II does not follow.Test III (Some songs are tapes): Similarly, the some cassettes–songs overlap may be with cassettes that are not discs, whereas tapes overlap a different portion of discs. Hence III does not follow.Test IV (No song is a disc): A total exclusion is even stronger and is not implied; songs could be among the same cassettes that are also discs. IV does not follow. Verification / Alternative check:Draw Venn diagrams or pick concrete elements: let D1 overlap T (tapes) but not C (cassettes), let D2 overlap C but not T, and let S overlap a subset of C disjoint from D2. All premises remain true while I–IV can all be false. This proves none of the conclusions is forced. Why Other Options Are Wrong: Only either I or IV follows: neither I nor IV follows. Only either II or IV follows: neither follows. Only III and IV follow: both are unsupported. Only III and either II or IV follows: again, none of those are necessary. Common Pitfalls:Assuming transitivity for some; believing that three some links guarantee end-to-end overlap; treating absence of information as evidence of exclusion. Final Answer:None of these

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