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Difficulty: MediumAssumptions in Conditional Logic

Chief Engineer: A spacecraft's life-support system can sustain a crew during a deep-space voyage only if it features a regenerative carbon dioxide scrubber. Therefore, any spacecraft commissioned for the Outer Planets Initiative must feature a regenerative carbon dioxide scrubber.

Which one of the following is an assumption on which the chief engineer's argument depends?

  1. Every spacecraft commissioned for the Outer Planets Initiative requires a life-support system that can sustain a crew during a deep-space voyage.Answer
  2. B
    Any spacecraft that features a regenerative carbon dioxide scrubber is capable of sustaining a crew during a deep-space voyage.
  3. C
    Any spacecraft whose life-support system can sustain a crew during a deep-space voyage is commissioned for the Outer Planets Initiative.
  4. D
    Spacecraft that are not commissioned for the Outer Planets Initiative do not need to feature regenerative carbon dioxide scrubbers.
  5. E
    The primary objective of the Outer Planets Initiative is to test the viability of regenerative carbon dioxide scrubbers in deep space.

Answer

Every spacecraft commissioned for the Outer Planets Initiative requires a life-support system that can sustain a crew during a deep-space voyage.
The argument relies on conditional reasoning. The premise establishes that sustaining a crew in deep space requires a regenerative scrubber. The conclusion claims that spacecraft in the Outer Planets Initiative must have this scrubber. To logically connect the premise to the conclusion, the argument must assume that spacecraft in the Initiative are required to sustain a crew in deep space. Without this bridge, the premise about sustaining a crew would be entirely irrelevant to the Initiative's spacecraft.

Step-by-Step Solution

1
Identify the core conditional premise provided in the argument.
Sustain a crew in deep space -> Features a regenerative scrubber.
The phrase 'only if' introduces a necessary condition that must be met.
2
Identify the main conclusion drawn by the chief engineer.
Outer Planets Initiative spacecraft -> Features a regenerative scrubber.
The transition word 'Therefore' indicates the final claim the author is trying to prove.
3
Identify the logical gap between the premise and the conclusion.
The argument jumps from a requirement for sustaining a crew to a requirement for Outer Planets Initiative spacecraft.
To prove that the Initiative spacecraft need scrubbers, there must be a connecting link showing that these specific spacecraft are required to sustain a crew.
4
Formulate the necessary assumption and verify it using the Negation Test.
Assumption: Outer Planets Initiative spacecraft -> Sustain a crew. Negation: Some Initiative spacecraft do not need to sustain a crew. If the negation is true, the conclusion fails because those spacecraft wouldn't strictly need the scrubber.
The Negation Test confirms that this conditional bridge is an absolute logical requirement for the argument to hold.

Key Concept

Identifying necessary assumptions to bridge structural gaps in conditional reasoning chains.
Estimated Time:1m 30s
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Assumptions in Conditional Logic

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