Propagate the particular through the universal inclusion.
- Premise 1: Some hens are cows, so Hens ∩ Cows ≠ ∅.
- Premise 2: All cows are horses, so Cows ⊆ Horses.
- Conclusions: I. Some horses are hens. II. Some hens are horses.
Concept/ApproachElements in Hens ∩ Cows are automatically in Horses due to Cows ⊆ Horses.DerivationLet h be an element in Hens ∩ Cows. Since Cows ⊆ Horses, h is also in Horses. Therefore both Horses ∩ Hens and Hens ∩ Horses are non empty. So I and II follow.Verification/AlternativeExample: Hens = {h1, h2}, Cows = {h1}, Horses = {h1, x}. The witness h1 satisfies both conclusions.Common pitfallsMissing that a particular carries through a universal subset relation.Final AnswerBoth I and II follow.
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