Premises: (1) All pens are chalks (Pens ⊆ Chalks). (2) All chairs are chalks (Chairs ⊆ Chalks). Conclusions: (I) Some pens are chairs. (II) Some chalks are pens.
Concept/ApproachUniversal inclusion into the same superset does not force two subsets to overlap. But a valid immediate inference from ‘‘All S are P’’ is the particular ‘‘Some P are S’’ (assuming S exists).Test Conclusion IEven though both Pens and Chairs are inside Chalks, they could be disjoint subsets. Hence ‘‘Some pens are chairs’’ is not compelled. I does not follow.Test Conclusion IIFrom ‘‘All pens are chalks’’, we infer ‘‘Some chalks are pens’’ (at least one pen exists and is a chalk). Therefore II follows.Common pitfallsAssuming overlap between two different subclasses of the same class without evidence.Final AnswerOnly conclusion II follows.
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