Syllogism — Identify the necessary conclusion(s) Statements: All snakes are trees. Some trees are roads. All roads are mountains. Conclusions: (I) Some mountains are snakes. (II) Some roads are snakes. (III) Some mountains are trees.

Question

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

Accepted Answer

Introduction / Context:We are to deduce which conclusions must be true from the chain of subsets and an existential statement. Be careful not to overextend “some” beyond what is stated. Given Data / Assumptions: All Snakes are Trees (S ⊆ Tr). Some Trees are Roads (∃ Tr ∩ Rd). All Roads are Mountains (Rd ⊆ Mtn). Concept / Approach: Transitivity of “All”: if A ⊆ B and B ⊆ C, then A ⊆ C. “Some Trees are Roads” together with “Roads ⊆ Mountains” yields “Some Mountains are Trees.” But unless Snakes are directly linked to Roads, we cannot guarantee any Snake lies in Mountains via Roads. Step-by-Step Solution: From ∃(Tr ∩ Rd) and Rd ⊆ Mtn, we get ∃(Tr ∩ Mtn). Hence (III) “Some mountains are trees” necessarily follows.(I) “Some mountains are snakes” would require ∃(S ∩ Mtn). We only know S ⊆ Tr; we do not know that any Snakes are among the Trees which are also Roads. So (I) is not forced.(II) “Some roads are snakes” demands ∃(Rd ∩ S). We only have ∃(Rd ∩ Tr) and S ⊆ Tr, which does not guarantee any road-tree is a snake. Hence (II) does not follow. Verification / Alternative check: Construct a model where the Trees that are Roads are entirely distinct from the subset of Trees that are Snakes. Premises hold; (I) and (II) fail; (III) holds. Why Other Options Are Wrong: Options asserting (I) or (II) require extra overlap not provided by the premises. Common Pitfalls: Assuming that because S ⊆ Tr and some Tr are Rd, some S must be Rd. That is not logically necessary. Final Answer: Only III follows

Syllogism — Identify the necessary conclusion(s) Statements: All snakes are trees. Some trees are roads. All roads are mountains. Conclusions: (I) Some mountains are snakes. (II) Some roads are snakes. (III) Some mountains are trees.

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