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Difficulty: MediumSufficient Assumption

Match each of the following incomplete arguments with the sufficient assumption that, if added as a premise, would logically guarantee its conclusion.

  • Because the national transit subsidy was repealed, commuting costs for suburban residents will rise. Consequently, retail sales in suburban districts will sharply decline.Whenever suburban residents experience rising commuting costs, retail sales in their districts experience a sharp decline.
  • The soil in the eastern valley contains unusually high levels of iridium. Therefore, the valley must have been the site of a prehistoric meteorite impact.The only possible explanation for unusually high levels of iridium in soil is a prehistoric meteorite impact.
  • The proposed zoning ordinance will allow for the construction of high-density housing units. Thus, the ordinance will successfully reduce the city's average rent prices.Any policy that allows for the construction of high-density housing units will successfully reduce average rent prices.
  • The disciplinary board reached its verdict without allowing the accused to cross-examine witnesses. As a result, the board's verdict is procedurally invalid.No verdict reached without allowing the accused to cross-examine witnesses can be considered procedurally valid.

Answer

Argument 1 matches with the rising commuting costs assumption. Argument 2 matches with the iridium explanation assumption. Argument 3 matches with the high-density housing assumption. Argument 4 matches with the cross-examination assumption.
Each correct pairing provides the exact conditional relationship needed to bridge the logical gap in the argument. By explicitly stating that the premise condition guarantees the conclusion condition, the assumption renders the argument completely valid.

Step-by-Step Solution

1
Analyze each incomplete argument to identify the stated premise and the final conclusion.
Isolated the logical gap in each argument (e.g., in the first argument, the gap is between rising commuting costs and declining retail sales).
Identifying the gap is necessary to know what the missing bridge must be.
2
Scan the available assumptions for conditional statements that link the premise terms directly to the conclusion terms.
Found corresponding conditional or universal statements for each argument's specific vocabulary.
A sufficient assumption must guarantee the conclusion, typically by forming a direct logical link from the evidence to the claim.
3
Verify that applying the chosen assumption to the premise definitively proves the conclusion without any remaining loopholes.
Each matched assumption forces its respective conclusion to be true.
Ensures the assumption is logically sufficient rather than merely necessary.

Key Concept

Sufficient Assumption
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Topics

Sufficient Assumption

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