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Difficulty: MediumConditional Logic and Formal Deductions

Under municipal transit regulations, a technology firm receives a commercial testing permit for autonomous trucks on public highways only if its navigation software achieves a Tier-1 safety certification. Achieving a Tier-1 safety certification requires completing at least 500,000 miles of simulated urban driving without a single critical system disengagement. Furthermore, unless a firm holds a commercial testing permit, it is forbidden from deploying autonomous vehicles during peak traffic hours.

If the statements above are true, which of the following must also be true?

  1. A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.Answer
  2. B
    Any technology firm that completes 500,000 miles of simulated urban driving without a critical system disengagement will automatically receive a commercial testing permit.
  3. C
    A technology firm that has not been permitted to deploy autonomous vehicles during peak traffic hours has failed to achieve a Tier-1 safety certification.
  4. D
    Autonomous trucks that have logged 500,000 miles of simulated urban driving are safer than conventional commercial trucks operated by human drivers.
  5. E
    Technology firms holding a commercial testing permit deploy autonomous trucks exclusively during non-peak traffic hours.

Answer

A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.
The passage establishes a chain of necessary conditions: to deploy during peak traffic hours, a firm must hold a commercial testing permit; to have that permit, it must hold Tier-1 certification; and to achieve Tier-1 certification, it must complete 500,000 simulated miles without a critical disengagement. Therefore, any firm deploying vehicles during peak hours must have completed those 500,000 simulated miles.

Step-by-Step Solution

1
Formalize the conditional statements given in the passage
Statement 1: Commercial Permit -> Tier-1 Certification. Statement 2: Tier-1 Certification -> 500,000 Simulated Miles without critical disengagement. Statement 3: Deploy Peak Hours -> Commercial Permit.
Translating natural language indicators ('only if', 'requires', 'unless') into formal logic clarifies necessary and sufficient conditions.
2
Chain the conditional statements together transitively
Deploy Peak Hours -> Commercial Permit -> Tier-1 Certification -> 500,000 Simulated Miles.
Because each condition is necessary for the preceding one, the entire chain must hold true.
3
Deduce the logically necessary conclusion
Deploying during peak traffic hours necessarily implies having completed at least 500,000 miles of simulated driving without a critical disengagement.
If the antecedent of the chain is true, all necessary conditions down the chain must also be true.

Key Concept

Transitive Chaining of Necessary Conditions
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Topics

Conditional Logic and Formal Deductions

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