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Difficulty: MediumDiagramming Conditional Statements

To properly classify organisms within the newly discovered Solaria fungal ecosystem, botanists adhere to strict taxonomic rules. A specimen is categorized as a bioluminescent species only if it synthesizes the compound luciferyl. Moreover, no fungus in this ecosystem synthesizes luciferyl without also maintaining a symbiotic relationship with local root systems. Finally, exhibiting a rapid spore-dispersal mechanism requires that the fungus not maintain a symbiotic relationship with local root systems.

Based on the botanists' taxonomic rules, which one of the following statements must be true?

  1. Any specimen in the Solaria ecosystem that exhibits a rapid spore-dispersal mechanism is not categorized as a bioluminescent species.Answer
  2. B
    If a specimen in the ecosystem does not exhibit a rapid spore-dispersal mechanism, then it synthesizes the compound luciferyl.
  3. C
    Any specimen that synthesizes the compound luciferyl must be categorized as a bioluminescent species.
  4. D
    Any fungus that maintains a symbiotic relationship with local root systems must synthesize the compound luciferyl.
  5. E
    Most specimens that do not exhibit a rapid spore-dispersal mechanism are categorized as bioluminescent species.

Answer

The statement declaring that any specimen exhibiting a rapid spore-dispersal mechanism is not categorized as a bioluminescent species.
The stimulus provides three conditional statements. First: Bioluminescent -> Synthesizes luciferyl. Second: Synthesizes luciferyl -> Symbiotic relationship. Connecting these gives: Bioluminescent -> Synthesizes luciferyl -> Symbiotic relationship. The third statement is: Rapid spore-dispersal -> NO Symbiotic relationship. The contrapositive of this third statement is: Symbiotic relationship -> NO Rapid spore-dispersal. By attaching this contrapositive to the end of our initial chain, we establish a complete unbroken chain: Bioluminescent -> Synthesizes luciferyl -> Symbiotic relationship -> NO Rapid spore-dispersal. This proves that any bioluminescent species cannot have a rapid spore-dispersal mechanism. The contrapositive of this overarching deduction is that any fungus with rapid spore-dispersal is not bioluminescent. The correct answer choice explicitly states this valid contrapositive.

Step-by-Step Solution

1
Diagram the first sentence.
Bioluminescent -> Synthesizes luciferyl
The phrase 'only if' introduces a necessary condition.
2
Diagram the second sentence.
Synthesizes luciferyl -> Symbiotic relationship
The phrase 'no [X] without [Y]' means that X is sufficient to guarantee Y.
3
Diagram the third sentence.
Rapid spore-dispersal -> NO Symbiotic relationship
The word 'requires' introduces a necessary condition, which in this case is negative.
4
Form the logical chain.
Bioluminescent -> Synthesizes luciferyl -> Symbiotic relationship
The necessary condition of the first premise is the sufficient condition of the second.
5
Integrate the third premise into the chain via contraposition.
Symbiotic relationship -> NO Rapid spore-dispersal
The contrapositive of (Rapid spore-dispersal -> NO Symbiotic relationship) allows it to link to the end of our existing chain.
6
Make the final deduction.
Bioluminescent -> NO Rapid spore-dispersal. Contrapositive: Rapid spore-dispersal -> NO Bioluminescent.
By following the continuous directional arrows of the full chain, the first sufficient condition inevitably leads to the final necessary condition.

Key Concept

Diagramming Conditional Statements
Estimated Time:2m 0s
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Topics

Diagramming Conditional Statements

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