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Difficulty: HardSufficient Assumption

Environmental Policy Analyst: Any geothermal power station that utilizes closed-loop supercritical fluid extraction achieves an operational thermal efficiency exceeding forty percent. Furthermore, no geothermal facility operating at an efficiency exceeding forty percent qualifies for regional groundwater conservation credits unless it reinjects all extracted mineral condensates into deep sub-surface basalt formations. The North Ridge geothermal facility was recently awarded regional groundwater conservation credits. Therefore, the North Ridge facility does not utilize closed-loop supercritical fluid extraction.

The environmental policy analyst's conclusion follows logically if which one of the following is assumed?

  1. A
    Any geothermal facility that reinjects all extracted mineral condensates into deep sub-surface basalt formations achieves an operational thermal efficiency exceeding forty percent.
  2. B
    The North Ridge geothermal facility would not qualify for regional groundwater conservation credits if its operational thermal efficiency were below forty percent.
  3. The North Ridge geothermal facility does not reinject all extracted mineral condensates into deep sub-surface basalt formations.Answer
  4. D
    No geothermal power station that qualifies for regional groundwater conservation credits achieves an operational thermal efficiency below forty percent.
  5. E
    Closed-loop supercritical fluid extraction is the only extraction method that allows geothermal power stations to achieve an operational thermal efficiency exceeding forty percent.

Answer

The assumption that the North Ridge geothermal facility does not reinject all extracted mineral condensates into deep sub-surface basalt formations.
The argument contains a conditional gap between receiving conservation credits and not using supercritical fluid extraction. The premises establish that supercritical extraction requires efficiency exceeding forty percent, and that any facility exceeding forty percent efficiency that receives credits must reinject all extracted mineral condensates into basalt formations. Given that the North Ridge facility received these credits, assuming that it does not reinject all condensates into basalt formations logically necessitates that its efficiency cannot exceed forty percent (by modus tollens). Because its efficiency does not exceed forty percent, it cannot utilize closed-loop supercritical fluid extraction. Thus, the conclusion is deductively guaranteed.

Step-by-Step Solution

1
Analyze the premises and symbolize the formal conditional relationships in the argument.
Premise 1: Supercritical Extraction →\rightarrow Thermal Efficiency >40%> 40\%. Premise 2: Thermal Efficiency >40%> 40\% AND Conservation Credits →\rightarrow Basalt Reinjection. Premise 3: North Ridge received Conservation Credits.
Deconstructing the argument into formal logic isolates the exact inferential gap between the premises and the conclusion.
2
Determine what intermediate condition is required to reach the conclusion via contrapositive reasoning.
Conclusion to prove: North Ridge does NOT have Supercritical Extraction. By the contrapositive of Premise 1 (NOT Thermal Efficiency >40%→> 40\% \rightarrow NOT Supercritical Extraction), we need to establish that North Ridge does NOT have Thermal Efficiency >40%> 40\%.
A sufficient assumption must provide the missing premise that, combined with existing premises, deductively forces the intermediate and final conclusions.
3
Connect the credit status of North Ridge to the negation of the high-efficiency condition.
By Premise 2, if a facility has Thermal Efficiency >40%> 40\% and receives Conservation Credits, it MUST perform Basalt Reinjection. The contrapositive states: If a facility receives Conservation Credits and does NOT perform Basalt Reinjection, it CANNOT have Thermal Efficiency >40%> 40\%.
Since North Ridge received Conservation Credits, supplying the premise that it does NOT perform Basalt Reinjection forces the conclusion that its efficiency is not >40%> 40\%, which in turn proves it does not use Supercritical Extraction.

Key Concept

Sufficient Assumption in Conditional Reasoning Chains
Estimated Time:1m 30s
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Topics

Sufficient Assumption

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