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Difficulty: MediumAssumptions in Conditional Logic

The following arguments each rely on an unstated conditional premise to bridge their evidence to their conclusion. Match each argument with the strictly necessary conditional assumption that logically completes its reasoning.

  • The rare alpine orchids require soil with a highly specific mineral composition to survive in the biodome. Since the researchers have successfully synthesized soil that perfectly mimics this composition, it is guaranteed that the orchids will survive.Any orchid provided with soil that mimics the necessary mineral composition will survive in the biodome.
  • The city council refuses to raise commercial property taxes this fiscal year. Therefore, the new urban zoning initiative will fail to reduce downtown traffic congestion.A reduction in downtown traffic congestion cannot be achieved unless commercial property taxes are raised.
  • A corporation is subject to federal antitrust scrutiny only when its domestic market share exceeds forty percent. Apex Industries recently acquired its largest competitor, bringing its market share to forty-five percent. Consequently, Apex Industries will now face federal antitrust scrutiny.Every corporation that commands a domestic market share exceeding forty percent is subjected to federal antitrust scrutiny.
  • An action can be considered morally praiseworthy only if it is performed entirely out of a sense of duty. The altruistic actions performed by our local volunteers are motivated by deep empathy for others. Therefore, the actions of these volunteers are not morally praiseworthy.No action that is motivated by deep empathy for others is performed entirely out of a sense of duty.

Answer

Match the orchid argument with the assumption making synthesized soil sufficient for survival; match the traffic argument with the assumption making tax raises necessary for reducing congestion; match the antitrust argument with the assumption making market share sufficient for scrutiny; match the altruism argument with the assumption making empathy mutually exclusive with duty.
Each correct pairing provides the exact formal logical bridge required to make the conclusion of the corresponding argument valid, repairing illegal reversals, linking disparate terms, and forming logically sound contrapositives.

Step-by-Step Solution

1
Analyze the alpine orchids argument.
Identified the argument treats a necessary condition (mineral soil) as sufficient. Matches with the premise establishing that providing the soil guarantees survival.
To prove the conclusion that the orchids will survive, the necessary condition must be formally elevated to a sufficient condition.
2
Analyze the traffic congestion argument.
Identified a missing link between not raising taxes and not reducing congestion. Matches with the premise stating congestion cannot be reduced unless taxes are raised.
The conclusion relies on the contrapositive of the missing premise: If congestion is reduced, taxes are raised. Since taxes are not raised, congestion is not reduced.
3
Analyze the antitrust scrutiny argument.
Identified an illegal reversal involving 'only when'. Matches with the premise stating every corporation with over forty percent market share faces scrutiny.
The argument provides the necessary condition (forty-five percent share) but illicitly concludes the result. The assumption must dictate that the condition is sufficient to guarantee the result.
4
Analyze the moral praiseworthiness argument.
Identified two unconnected sufficient terms (empathy and duty). Matches with the premise stating empathy and duty are mutually exclusive.
To conclude an action is not praiseworthy because it lacks duty (since it was driven by empathy), the author must assume that having empathy means the action was not done entirely out of duty.

Key Concept

Identifying unstated conditional premises and recognizing illegal reversals (confusing necessary and sufficient conditions) in logical arguments.
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Topics

Assumptions in Conditional Logic

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