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Difficulty: MediumMust Be True / Most Strongly Supported

In the Northern Cascade mountain range, any high-elevation forest plot that sustains a breeding population of northern spotted owls contains old-growth Douglas fir trees. Every forest plot containing old-growth Douglas fir trees has a canopy closure rate of at least 70 percent. However, no forest plot with a canopy closure rate of at least 70 percent permits the rapid proliferation of sun-loving invasive thistle species. In last year's ecological survey of the region, Plot K was found to have a rapid proliferation of sun-loving invasive thistle species.

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

  1. A
    Any forest plot in the Northern Cascade range that does not sustain a breeding population of northern spotted owls will experience a rapid proliferation of sun-loving invasive thistle species.
  2. B
    A canopy closure rate of at least 70 percent is sufficient to guarantee that a forest plot sustains a breeding population of northern spotted owls.
  3. Plot K does not sustain a breeding population of northern spotted owls.Answer
  4. D
    Every forest plot in the Northern Cascade mountain range with a canopy closure rate below 70 percent is completely overrun by invasive thistle species.
  5. E
    Forest plots in the Northern Cascade range that lack old-growth Douglas fir trees are incapable of supporting any avian wildlife species.

Answer

Plot K does not sustain a breeding population of northern spotted owls.
The stimulus provides a three-step conditional rule: sustaining breeding spotted owls requires old-growth Douglas firs, which require a canopy closure of at least 70 percent, which in turn prevents rapid thistle proliferation. Taking the contrapositive of this entire chain demonstrates that any plot exhibiting rapid thistle proliferation cannot sustain breeding spotted owls. Since Plot K has rapid thistle proliferation, it strictly follows that Plot K does not sustain a breeding population of northern spotted owls.

Step-by-Step Solution

1
Formalize the conditional relationships provided in the stimulus.
Breeding Spotted Owls →\rightarrow Old-Growth Douglas Firs →\rightarrow Canopy Closure ≥70%→\ge 70\% \rightarrow No Rapid Thistle Proliferation.
Mapping the premises into standard formal logic allows for unambiguous chaining of sufficient and necessary conditions.
2
Derive the contrapositive of the full conditional chain.
Rapid Thistle Proliferation →\rightarrow Canopy Closure <70%→< 70\% \rightarrow No Old-Growth Douglas Firs →\rightarrow No Breeding Spotted Owls.
The contrapositive of any valid conditional relationship is logically equivalent and must also be true.
3
Apply the specific factual observation regarding Plot K to the contrapositive chain.
Plot K has rapid thistle proliferation, which deductively proves that Plot K cannot sustain a breeding population of northern spotted owls.
Executing modus tollens with the confirmed existence of thistles in Plot K guarantees the conclusion.

Key Concept

Deductive Conditional Chaining and Contrapositive Inference
Estimated Time:1m 15s
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Topics

Must Be True / Most Strongly Supported

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