Question

Difficulty: MediumSufficient Assumption

Match each flawed argument with the sufficient assumption that logically guarantees its conclusion. Consider contrapositives and conditional translations carefully.

  • Argument 1: The proposed budget cuts will drastically reduce funding for the arts program. Therefore, the budget cuts will harm the intellectual development of the students.If an administrative action does not harm the intellectual development of students, then it does not reduce funding for the arts program.
  • Argument 2: To qualify as a historical landmark, a building must have been constructed before 1920. The abandoned textile mill was built in 1934. Thus, the mill cannot be exempted from the new property tax.Any structure that is granted an exemption from the new property tax must have been constructed prior to 1920.
  • Argument 3: The novel's protagonist acts out of pure self-interest rather than a sense of moral duty. Hence, the novel cannot be classified as a traditional tragedy.A literary work can be classified as a traditional tragedy only if its protagonist does not act out of pure self-interest.
  • Argument 4: The governor's transit initiative relies heavily on privatized toll roads. Therefore, the initiative will disproportionately burden low-income commuters.No public transportation initiative can rely heavily on privatized toll roads unless it disproportionately burdens low-income commuters.

Answer

Each argument must be matched with the assumption that perfectly bridges the gap between its premises and conclusion, often presented as a contrapositive or through advanced conditional terminology like 'unless' or 'only if'.
Each correct pair matches an argument with a missing logical link to the rule that perfectly bridges that gap. The matching assumptions utilize contrapositives and complex conditional phrasing (e.g., 'only if', 'unless') to state the required bridges logically.

Step-by-Step Solution

1
Analyze Argument 1's logical gap.
The gap is between reducing arts funding and harming intellectual development.
To guarantee the conclusion, we need a premise stating that reducing arts funding causes intellectual harm.
2
Identify the assumption for Argument 1.
The correct match is the statement that provides the contrapositive of the needed rule.
The statement 'If not harming development -> not reducing funding' is logically equivalent to 'If reducing funding -> harming development'.
3
Analyze Argument 2's structure.
Premise: Landmark -> Built before 1920. The mill is NOT built before 1920. Conclusion: The mill is NOT exempted.
The missing link must logically connect being exempted to being built before 1920.
4
Identify the assumption for Argument 2.
The matching assumption states 'Exempted -> Built before 1920'.
Since the mill fails the necessary condition (built before 1920), it cannot be exempted, perfectly guaranteeing the conclusion.
5
Analyze Argument 3's gap.
Premise: Protagonist acts out of self-interest. Conclusion: Not a traditional tragedy.
We need the rule 'Self-interest -> Not traditional tragedy'.
6
Identify the assumption for Argument 3.
The statement 'Traditional tragedy only if not self-interest' translates to 'Traditional tragedy -> Not self-interest'.
This is the contrapositive of the required premise, validating the argument.
7
Analyze Argument 4's gap and matching assumption.
Gap: Toll roads -> Burdens commuters. The match uses 'No X unless Y' format.
The statement 'No initiative relies on toll roads unless it burdens commuters' means 'If it relies on toll roads, it burdens commuters', which bridges the gap.

Key Concept

Sufficient Assumption Conditional Mapping
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