Two step inclusion chain: ‘‘All huts are mansions’’ and ‘‘All mansions are temples’’ — determine which particular conclusions about temples containing huts and mansions necessarily hold.

Question

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

Curioustab · Accepted Answer

Classic chain of inclusion yields immediate particular consequences when classes are non empty. Premise 1: Huts ⊆ Mansions. Premise 2: Mansions ⊆ Temples. Hence Huts ⊆ Temples and Mansions ⊆ Temples. Concept/ApproachFrom All S are P we may infer Some P are S provided S is non empty. Syllogism problems typically assume non empty terms unless stated otherwise.Deriving conclusionsI. Some temples are huts: since Huts ⊆ Temples and huts exist, pick any hut; it is a temple.II. Some temples are mansions: similarly, pick any mansion; it is a temple.Verification/AlternativeExample: Huts = {h1}, Mansions = {h1, m2}, Temples = {h1, m2, t3}. Both conclusions are witnessed by h1 and m2 respectively.Common pitfallsForgetting the existence assumption behind particular conclusions that are derived from universal inclusions.Final AnswerBoth I and II follow.