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Zorluk: OrtaForming Contrapositives

Under the new municipal zoning code, obtaining a commercial building permit requires that the developer submit a comprehensive environmental impact report and secure approval from the local neighborhood council.

Which one of the following statements logically follows from the zoning code requirements?

  1. If a developer fails to secure approval from the local neighborhood council, they will not obtain a commercial building permit, even if they have submitted a comprehensive environmental impact report.Cevap
  2. B
    If a developer submits a comprehensive environmental impact report and secures approval from the local neighborhood council, they will obtain a commercial building permit.
  3. C
    If a developer does not obtain a commercial building permit, it must be because they failed to either submit a comprehensive environmental impact report or secure approval from the local neighborhood council.
  4. D
    Failing to submit a comprehensive environmental impact report guarantees that the developer will not secure approval from the local neighborhood council.
  5. E
    A developer will fail to obtain a commercial building permit only if they fail to both submit a comprehensive environmental impact report and secure approval from the local neighborhood council.

Cevap

The correct answer states that failing to secure approval from the local neighborhood council guarantees the developer will not obtain a commercial building permit, even if the other requirement is met.
The stimulus establishes a rule where obtaining a permit requires two separate necessary conditions: submitting a report AND getting council approval. According to formal logic, if a sufficient condition requires a compound necessary condition (A -> B and C), the contrapositive dictates that failing either necessary condition guarantees the sufficient condition cannot occur (~B or ~C -> ~A). Therefore, a developer who fails to get council approval will definitively not get a permit, regardless of whether they submitted the report.

Adım Adım Çözüm

1
Identify the conditional relationship in the stimulus.
Obtaining a permit (Sufficient) -> Submit environmental report AND secure council approval (Necessary).
The phrase 'requires that' introduces necessary conditions for the event that precedes it.
2
Form the contrapositive using De Morgan's laws.
If a developer does NOT submit the report OR does NOT secure council approval -> they will NOT obtain a permit.
To create a valid contrapositive, negate both sides and reverse their order. When negating an 'AND' statement, it becomes an 'OR' statement.
3
Evaluate the answer choices against the deduced contrapositive.
The correct choice matches one half of the 'OR' condition in the contrapositive.
Because failing either one of the necessary conditions is sufficient to prevent obtaining the permit, lacking council approval guarantees denial of the permit.

Anahtar Kavram

Forming contrapositives from compound conditional statements (De Morgan's Laws).
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Konular

Forming Contrapositives

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