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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.

Difficulty: Medium

Correct Answer: Both I and II follow

Explanation:

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/Approach
From 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 conclusions
I. 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/Alternative
Example: Huts = {h1}, Mansions = {h1, m2}, Temples = {h1, m2, t3}. Both conclusions are witnessed by h1 and m2 respectively.
Common pitfalls
Forgetting the existence assumption behind particular conclusions that are derived from universal inclusions.
Final Answer
Both I and II follow.
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