Question

Difficulty: EasyDrawing Valid Inferences

A botanical survey of an alpine valley established that the blue alpine gentian blooms exclusively at elevations above 2,5002,500 meters. Researchers also determined that the mountain bumblebee, which serves as the sole pollinator for the blue alpine gentian, cannot survive in habitats where the average summer temperature exceeds 15C15^\circ\text{C}. Over the past decade, average summer temperatures across all areas of the valley situated between 2,2002,200 meters and 2,6002,600 meters in elevation have consistently exceeded 15C15^\circ\text{C}.

If the statements above are true, which of the following must also be true on the basis of them?

  1. Blue alpine gentians growing between 2,5002,500 meters and 2,6002,600 meters in elevation have lacked their sole pollinator over the past decade.Answer
  2. B
    Mountain bumblebees have migrated to elevations above 2,8002,800 meters in order to find cooler summer temperatures.
  3. C
    The blue alpine gentian will become entirely extinct throughout the alpine valley within the next decade.
  4. D
    Average summer temperatures at elevations below 2,2002,200 meters remained strictly at or below 15C15^\circ\text{C} during the past decade.
  5. E
    The rise in summer temperatures between 2,2002,200 and 2,6002,600 meters was caused by recent changes in regional wind patterns.

Answer

Blue alpine gentians growing between 2,500 meters and 2,600 meters in elevation have lacked their sole pollinator over the past decade.
The passage establishes three facts: gentians bloom above 2,500 meters, bumblebees (their sole pollinator) cannot survive when summer temperatures exceed 15°C, and temperatures exceeded 15°C between 2,200 and 2,600 meters over the past decade. Combining these facts proves that in the elevation interval from 2,500 to 2,600 meters, temperatures were too high for bumblebees to survive, meaning gentians in that specific band lacked their pollinator.

Step-by-Step Solution

1
Identify the overlapping elevation range in the premises.
Gentians grow above 2,500 m2,500\text{ m}. Temperatures exceeded 15C15^\circ\text{C} between 2,200 m2,200\text{ m} and 2,600 m2,600\text{ m}. The overlapping zone is 2,500 m2,500\text{ m} to 2,600 m2,600\text{ m}.
Deducting valid inferences requires combining facts that share common boundary conditions.
2
Apply the temperature constraint to pollinator survival in the overlapping zone.
Because temperatures in the 2,500 m2,500\text{ m}2,600 m2,600\text{ m} zone exceeded 15C15^\circ\text{C}, mountain bumblebees could not survive there during the past decade.
The premise states bumblebees cannot survive where average summer temperatures exceed 15C15^\circ\text{C}.
3
Synthesize the conclusion regarding the gentian flower.
Any blue alpine gentians blooming in the 2,500 m2,500\text{ m}2,600 m2,600\text{ m} zone were in an environment where their sole pollinator could not survive.
Combining the presence condition of gentians with the absence condition of bumblebees yields a logically unavoidable inference.

Key Concept

Drawing Valid Inferences via Set Intersection
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