Question

Difficulty: MediumDrawing Valid Inferences

Ecological surveys conducted in High Alps alpine meadows revealed that any meadow with fewer than four native flowering plant species invariably experiences severe soil erosion during annual snowmelts. Conversely, every meadow containing at least four native flowering plant species maintains stable topsoil during annual snowmelts, provided that livestock grazing is strictly prohibited. Furthermore, whenever livestock grazing is strictly prohibited in a meadow, its soil nitrate retention remains above eighty percent, regardless of the number of plant species present.

Based on the information above, which of the following statements must be true? Select all that apply.

  1. Any High Alps meadow that maintained stable topsoil during an annual snowmelt contained at least four native flowering plant species.Answer
  2. B
    Any High Alps meadow with a soil nitrate retention above eighty percent will maintain stable topsoil during annual snowmelts.
  3. A High Alps meadow where livestock grazing was strictly prohibited that nevertheless experienced severe soil erosion during an annual snowmelt contained fewer than four native flowering plant species.Answer

Answer

The statements asserting that maintaining stable topsoil requires at least four native species, and that a meadow with prohibited grazing that experiences erosion must contain fewer than four native species, are both logically unavoidable.
The statement regarding meadows maintaining stable topsoil is valid because the passage establishes that having fewer than four species strictly leads to erosion; thus, avoiding erosion necessitates at least four species. The statement regarding a grazed-prohibited meadow experiencing erosion is valid because four or more species alongside prohibited grazing guarantees stability; experiencing erosion under prohibited grazing logically forces the species count to be fewer than four.

Step-by-Step Solution

1
Analyze the first formal premise and derive its contrapositive.
Premise 1: Fewer than 4 species → Severe erosion. Contrapositive: Stable topsoil (No severe erosion) → At least 4 species.
The contrapositive of a valid conditional statement is always logically equivalent and valid.
2
Analyze the second formal premise regarding combined conditions.
Premise 2: (At least 4 species) AND (Grazing prohibited) → Stable topsoil. Contrapositive: Severe erosion → (Fewer than 4 species) OR (Grazing permitted).
If stable topsoil requires both conditions to fail to occur, then severe erosion occurring when grazing is prohibited forces the remaining condition (species count) to be fewer than four.
3
Evaluate third condition and check for false equivalences.
Nitrate retention > 80% indicates prohibited grazing, but prohibited grazing is insufficient on its own to prevent erosion without at least 4 species.
High nitrate retention does not guarantee topsoil stability if species count is below four.

Key Concept

Drawing Valid Inferences via Conditional Logic Contrapositives
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