Difficulty: Medium
Correct Answer: Only (1) and (4)
Explanation:
Introduction / Context:Syllogism questions test whether a conclusion must be true based strictly on the given statements. We cannot add outside facts, and we must avoid assuming overlaps unless they are logically compelled by the premises.
Given Data / Assumptions:
Concept / Approach:Use classic set/venn reasoning. “All X are Y” means X is a subset of Y. “Some X are Y” indicates a definite non-empty intersection. Only conclusions that must hold for all diagrams consistent with the premises are valid.
Step-by-Step Solution:
From “Some answers are writers,” we can also say “Some writers are answers.” This validates conclusion (1).All writers are poets. The “some answers that are writers” are therefore also poets. Hence there exist entities that are both poets and answers, validating conclusion (4).For (2): Some poets are questions? We know some questions are answers, and some answers are writers, but the two “some” groups need not be the same individuals. An overlap between “questions” and “writers” (and thus poets) is not guaranteed. Hence (2) does not necessarily follow.For (3): All questions are poets is far stronger than warranted. We only know “some questions are answers,” not that all questions connect to writers/poets. So (3) is invalid.Verification / Alternative check:Draw Venn sets for Questions (Q), Answers (A), Writers (W), and Poets (P) with W entirely inside P. Place one element in A∩W (proves (1) and (4)). Place a separate element in Q∩A that is not in W. This diagram satisfies premises while falsifying (2) and (3).
Why Other Options Are Wrong:
Common Pitfalls:Assuming that “some … are …” chains guarantee overlap across multiple “some” statements. They do not. Only a single “all” statement permits a definite subset relation.
Final Answer:Only (1) and (4)
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