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Question

Difficulty: MediumStatement and Conclusions or Inferences

Statements:
1. Only infrastructure projects that pass the comprehensive seismic safety audit are granted a municipal construction permit.
2. The proposed Zenith Bridge project was not granted a municipal construction permit.

Conclusion: The proposed Zenith Bridge project did not pass the comprehensive seismic safety audit.

Assertion to evaluate: The given conclusion logically and necessarily follows from the provided statements.

Answer: Answer

Answer

False
The conclusion is false because it commits the logical fallacy of denying the antecedent. Just because passing the audit is a strict requirement to get a permit does not mean that every project without a permit failed the audit; they could have been rejected for entirely unrelated reasons.

Step-by-Step Solution

1
Analyze Statement 1 to identify the formal logical relationship.
The phrase 'Only [A] are [B]' means that [A] is a necessary condition for [B]. Thus, passing the audit is required for getting a permit, but it does not guarantee one.
Accurately identifying necessary versus sufficient conditions is critical for logical deduction.
2
Evaluate Statement 2 in relation to the established condition.
Statement 2 establishes that the Zenith Bridge project did not receive a permit.
Applying the specific scenario to the general rule.
3
Determine if the Conclusion is an absolute certainty based on the facts.
Knowing the project did not receive a permit does not allow us to conclude it failed the audit. It might have passed the audit but been denied the permit due to funding, zoning, or other separate issues.
Logical validity requires a conclusion to be necessarily true in all possible scenarios, which fails here.

Key Concept

Logical Deduction and Necessary vs. Sufficient Conditions

Alternative Method

Translate the statements into formal symbolic logic: Let P represent 'granted a permit' and A represent 'passed the audit'. Statement 1 (Only A are P) translates to P → A (If granted permit, then passed audit). Statement 2 is ~P (not P). The conclusion asserts ~A. Concluding ~A from P → A and ~P is formally invalid (the fallacy of denying the antecedent).
Estimated Time:1m 0s
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Topics

Statement and Conclusions or Inferences

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