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Difficulty: Very hardQuantifier Logic (Some, Most, All)

Marine biologists studying the newly discovered Marianas deep-sea caldera have cataloged various unique species. According to their findings, all organisms that inhabit the caldera's core depend entirely on chemosynthesis for survival. Furthermore, most of the organisms inhabiting the caldera's core lack photobiological receptors. Interestingly, any organism that migrates to the epipelagic zone possesses photobiological receptors. Finally, researchers noted that some organisms dependent on chemosynthesis are active filter feeders.

Which one of the following logically follows from the researchers' findings?

  1. A
    Most organisms that depend entirely on chemosynthesis do not migrate to the epipelagic zone.
  2. At least some organisms that depend entirely on chemosynthesis do not migrate to the epipelagic zone.Answer
  3. C
    Some active filter feeders lack photobiological receptors.
  4. D
    None of the organisms that inhabit the caldera's core migrate to the epipelagic zone.
  5. E
    Any organism that possesses photobiological receptors migrates to the epipelagic zone.

Answer

At least some organisms that depend entirely on chemosynthesis do not migrate to the epipelagic zone.
The correct answer properly chains the provided formal logic. Since any organism that migrates possesses photobiological receptors (Migrate →\rightarrow Receptors), it logically follows via contrapositive that any organism lacking these receptors does not migrate (No Receptors →\rightarrow No Migrate). We are told that most caldera core inhabitants lack these receptors; therefore, most caldera core inhabitants do not migrate. Finally, because all caldera core inhabitants depend entirely on chemosynthesis, this specific non-migrating group forms a part of the chemosynthesis-dependent population. Thus, it must be true that at least some organisms dependent on chemosynthesis do not migrate.

Step-by-Step Solution

1
Diagram the formal relationships provided in the stimulus.
1. Core →\rightarrow Chemosynthesis. 2. Core (most) →\rightarrow No Receptors. 3. Migrate →\rightarrow Receptors. 4. Chemosynthesis (some) →\rightarrow Filter Feeder.
Mapping the exact logical quantifiers prevents relying on outside assumptions and highlights formal connections.
2
Find the contrapositive of the strict conditional regarding migration.
If Migrate →\rightarrow Receptors, then No Receptors →\rightarrow No Migrate.
Contrapositives allow us to connect negative premises to strict conditional rules.
3
Chain the 'most' statement with the contrapositive.
Core (most) →\rightarrow No Receptors →\rightarrow No Migrate. Therefore, most Core inhabitants do not migrate.
A 'most' statement can be validly chained into a strict sufficient/necessary conditional to yield a new 'most' deduction.
4
Combine the deduction with the first premise to find the overlapping subset.
All Core inhabitants are Chemosynthesis-dependent. Since most Core inhabitants do not migrate, at least some Chemosynthesis-dependent organisms do not migrate.
If a subset (Core) has a certain property (No Migrate), and that entire subset belongs to a larger group (Chemosynthesis), then at least some members of the larger group must have that property.

Key Concept

Chaining 'most' statements with conditional contrapositives and inferring 'some' from subset relationships.
Estimated Time:2m 0s
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Topics

Quantifier Logic (Some, Most, All)

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