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Difficulty: HardDiagramming Conditional Statements

According to the Galactic Trade Federation's new charter, a planet's trading status is upgraded to 'Prime' only if its government both abolishes tariffs and implements comprehensive environmental protections. Furthermore, implementing comprehensive environmental protections requires that the planet either transitions to renewable energy or imposes strict carbon quotas. However, no planet imposes strict carbon quotas without facing immediate economic sanctions.

Which one of the following statements can be properly inferred from the rules of the Galactic Trade Federation charter?

  1. Any planet whose trading status is upgraded to 'Prime' and does not face immediate economic sanctions must transition to renewable energy.Answer
  2. B
    If a planet abolishes tariffs and implements comprehensive environmental protections, its trading status will be upgraded to 'Prime'.
  3. C
    If a planet's trading status is not upgraded to 'Prime', its government will neither abolish tariffs nor implement comprehensive environmental protections.
  4. D
    Most planets that transition to renewable energy will not face immediate economic sanctions.
  5. E
    Abolishing tariffs is a sufficient condition for a planet to implement comprehensive environmental protections.

Answer

The statement regarding a planet that achieves 'Prime' status and avoids immediate economic sanctions transitioning to renewable energy.
The stimulus provides a chain of conditional relationships. First, 'Prime' status requires implementing comprehensive environmental protections. Second, implementing these protections requires either transitioning to renewable energy or imposing strict carbon quotas. Third, imposing quotas always leads to facing immediate economic sanctions. If we know a planet achieves 'Prime' status, it must implement protections. Because it does not face economic sanctions, we know from the contrapositive of the third rule that it did not impose quotas. Therefore, to fulfill the requirement of implementing protections, the planet is left with only one logical pathway: it must transition to renewable energy. The correct answer accurately represents this valid deductive chain.

Step-by-Step Solution

1
Diagram the first conditional statement regarding the 'Prime' status.
Prime -> Abolish Tariffs (AT) AND Implement Protections (IP)
The phrase 'only if' introduces necessary conditions. For a planet to be upgraded to Prime, both AT and IP must occur.
2
Diagram the second conditional statement regarding environmental protections.
IP -> Transition to Renewable (TR) OR Impose Quotas (IQ)
The word 'requires' introduces a necessary condition, which in this case is a compound 'or' statement.
3
Diagram the third conditional statement and derive its contrapositive.
IQ -> Face Sanctions (FS). Contrapositive: ~FS -> ~IQ.
The phrase 'no [A] without [B]' translates to 'If A, then B'. The contrapositive reverses and negates the terms.
4
Chain the deductions together assuming a planet is Prime and does not face sanctions.
Prime -> IP -> TR OR IQ. Since ~FS -> ~IQ, the IQ option is eliminated. Thus, Prime AND ~FS -> TR.
Applying the rules to a Prime planet that avoids sanctions leaves transitioning to renewable energy as the only logical outcome to satisfy the environmental protections requirement.

Key Concept

Diagramming Conditional Statements and Formal Logic Chaining
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Topics

Diagramming Conditional Statements

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