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Difficulty: HardCannot Be True Questions

If a wetland area is designated as a Tier 1 Reserve, it must contain either endangered amphibian habitats or pristine coral structures. Any wetland area containing pristine coral structures is strictly protected from commercial fishing. The recently evaluated Oakhaven Estuary is designated as a Tier 1 Reserve, yet it is not strictly protected from commercial fishing.

If the statements above are true, which one of the following cannot be true?

  1. A
    There is a wetland area that is strictly protected from commercial fishing but does not contain pristine coral structures.
  2. B
    There exists a wetland area containing endangered amphibian habitats that is not designated as a Tier 1 Reserve.
  3. Oakhaven Estuary lacks endangered amphibian habitats.Answer
  4. D
    Commercial fishing poses a more significant ecological threat to pristine coral structures than to endangered amphibian habitats.
  5. E
    Most wetland areas that contain pristine coral structures are also designated as Tier 1 Reserves.

Answer

The statement that Oakhaven Estuary lacks endangered amphibian habitats cannot be true, as logical deduction proves it must contain them.
The correct answer explicitly contradicts a valid deduction made from the stimulus. Since Oakhaven is a Tier 1 Reserve, it must contain either amphibian habitats or coral structures. Because it is not strictly protected from commercial fishing, the contrapositive of the second premise dictates that it cannot contain coral structures. Therefore, it is mathematically required to contain endangered amphibian habitats. A statement claiming it lacks these habitats is logically impossible.

Step-by-Step Solution

1
Translate the first sentence into formal conditional logic.
Tier 1 Reserve →\rightarrow (Endangered Amphibian Habitats ∨\lor Pristine Coral Structures)
This establishes the necessary conditions for any wetland to be classified as a Tier 1 Reserve.
2
Translate the second sentence into formal conditional logic.
Pristine Coral Structures →\rightarrow Strictly Protected
This establishes the necessary condition for any wetland containing pristine coral structures.
3
Apply the contrapositive of the second condition to the facts provided about Oakhaven Estuary.
Since Oakhaven is NOT strictly protected, it CANNOT contain pristine coral structures (¬\neg Strictly Protected →\rightarrow ¬\neg Pristine Coral).
By the law of contrapositive, if the necessary condition is not met, the sufficient condition cannot be true.
4
Combine the deduction from Step 3 with the first conditional statement regarding Oakhaven Estuary.
Oakhaven is a Tier 1 Reserve, so it must have Amphibian Habitats OR Coral Structures. Since it lacks Coral Structures, it MUST have Endangered Amphibian Habitats.
In an 'either/or' framework, if one option is eliminated, the remaining option must be true.
5
Evaluate the answer choices to find the one that contradicts the established facts.
The option stating Oakhaven Estuary lacks endangered amphibian habitats directly contradicts the deduction in Step 4.
A 'Cannot Be True' question asks for the single choice that is logically impossible given the premises.

Key Concept

Deductive reasoning and contrapositives in multi-step conditional logic.
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