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Soru

Zorluk: OrtaStatement and Conclusions or Inferences

Statements:
1. All sustainable urban infrastructure projects receive prioritized federal funding.
2. No prioritized federal funding is allocated without a comprehensive environmental impact audit.

Conclusions:
I. All sustainable urban infrastructure projects require a comprehensive environmental impact audit.
II. Some projects that receive prioritized federal funding operate without a comprehensive environmental impact audit.

It is a logically valid deduction that only Conclusion I follows from the given statements.

Cevap: Cevap

Cevap

True
The final assertion is true because it correctly identifies that only Conclusion I is logically derived from the premises via the transitive property, while Conclusion II is a direct violation of Statement 2.

Adım Adım Çözüm

1
Translate the given statements into formal logical relationships.
Statement 1: Sustainable Project → Prioritized Funding. Statement 2: Prioritized Funding → Environmental Audit.
Establishing clear conditional logic helps prevent assumption-based errors and clarifies the boundaries of the premises.
2
Evaluate the validity of Conclusion I.
Conclusion I states: Sustainable Project → Environmental Audit. This is valid based on the transitive property of the two statements.
Direct syllogistic reasoning confirms that the necessary conditions cascade correctly from the first to the second statement.
3
Evaluate the validity of Conclusion II.
Conclusion II claims that Prioritized Funding can occur without an Environmental Audit. This explicitly contradicts Statement 2. Thus, Conclusion II is invalid.
Identifying direct contradictions ensures invalid conclusions are immediately dismissed.
4
Assess the final overarching claim presented in the stem.
The claim asserts that 'only Conclusion I follows'. Since Conclusion I is valid and Conclusion II is invalid, this claim evaluates to True.
The final truth value depends on the accurate evaluation of both individual conclusions against the overarching statement.

Anahtar Kavram

Syllogistic Reasoning and Transitive Logic
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Konular

Statement and Conclusions or Inferences

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