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Difficulty: MediumAssumptions in Conditional Logic

Analyze the following arguments, each of which relies on an unstated assumption involving conditional logic. Match each argument to the necessary or sufficient assumption that logically bridges the gap between its premises and its conclusion.

  • The metropolitan area will drastically reduce its carbon footprint if commuters adopt mass transit en masse. The city council's newly approved subsidy plan aggressively targets suburban train ticket prices. Therefore, the metropolitan area will drastically reduce its carbon footprint.Any municipal plan that aggressively targets suburban train ticket prices will successfully persuade commuters to adopt mass transit en masse.
  • A geological fault line is highly active only if it registers micro-tremors on a weekly basis. The Cascade fault system is known to be highly active. Therefore, the Cascade fault system must have recently exhibited significant geothermal venting.If a fault system does not exhibit significant geothermal venting, it does not register micro-tremors on a weekly basis.
  • The university's endowment will grow significantly this year. After all, the endowment grows significantly whenever alumni donations increase, and the university recently launched a highly praised career networking platform.Launching a highly praised career networking platform guarantees an increase in alumni donations.
  • A renewable energy grid cannot be considered stable unless it includes massive battery storage facilities. Therefore, the coastal wind farm project's new grid will not be considered stable, because it relies heavily on short-term federal grants.Any energy project that relies heavily on short-term federal grants fails to include massive battery storage facilities.

Answer

Argument 1 matches with the commuter subsidy bridge; Argument 2 matches with the contrapositive linking venting to tremors; Argument 3 matches with the platform-to-donations guarantee; and Argument 4 matches with the federal grants to battery storage connection.
Each correct pair seamlessly connects the factual premise of the argument to the conditional trigger required to validate the conclusion. When necessary, the assumption is presented in its logically equivalent contrapositive form (as seen in the geology argument).

Step-by-Step Solution

1
Map the formal logic of each argument's premises and conclusion.
Identify the conditional triggers: 'if' (sufficient), 'only if' (necessary), 'whenever' (sufficient), and 'unless' (necessary).
Accurately diagramming the stated conditions is required before the missing link can be identified.
2
Identify the 'dangling' terms in the premises and conclusion to find the logical gap.
For example, in the geological argument, the premises arrive at 'registers micro-tremors', but the conclusion introduces 'geothermal venting'.
The correct assumption must perfectly bridge these unmatched terms without introducing outside information.
3
Evaluate the assumption choices for direct conditional links or logically equivalent contrapositives.
The geological gap (Micro-tremors -> Geothermal Venting) is satisfied by finding its contrapositive (No Venting -> No Micro-tremors) in the available choices.
Test makers frequently hide the correct bridging assumption by stating it in its contrapositive form.

Key Concept

Bridging logical gaps using sufficient/necessary assumptions and recognizing their contrapositives.
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Topics

Assumptions in Conditional Logic

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