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Zorluk: OrtaStatement and Conclusions or Inferences

Analyze the two statements below and the subsequent conclusions to determine logical validity.

Statement I: The municipal zoning authority has ruled that any newly constructed commercial complex with a footprint exceeding 50,00050,000 square feet must allocate a minimum of 15%15\% of its total ground area to public recreational spaces.
Statement II: A consortium of major real estate developers recently suspended the construction of their planned 80,00080,000 square feet commercial projects.

Conclusion I: The developers suspended their projects specifically because they were unwilling to comply with the 15%15\% public recreational space mandate.
Conclusion II: Any newly constructed commercial complex that legally allocates only 10%10\% of its ground area to public recreational spaces must have a footprint of 50,00050,000 square feet or less.

Which of the given conclusions logically follows from the statements?

  1. A
    Only Conclusion I follows
  2. Only Conclusion II followsCevap
  3. C
    Both Conclusion I and Conclusion II follow
  4. D
    Neither Conclusion I nor Conclusion II follows

Cevap

The correct option is that Only Conclusion II follows.
Conclusion II is a valid deduction because it represents the contrapositive of Statement I. Statement I creates a rule: If Area > 50,00050,000, then Recreation ≥15%\ge 15\%. Conclusion II tests the inverse: if Recreation is only 10%10\% (which is <15%< 15\%), then the Area cannot be >50,000> 50,000. Conclusion I is invalid because the text never explicitly states why the developers suspended their projects; inferring their motivation is an assumption, not a logical deduction.

Adım Adım Çözüm

1
Analyze Statement I to extract logical rules and boundaries.
Identified the conditional rule: If a complex is greater than 50,00050,000 square feet, then it must allocate at least 15%15\% to recreational spaces.
To establish the primary logical parameters that govern the scenario.
2
Evaluate Conclusion I against the provided statements.
Conclusion I is invalid. While Statement II confirms that large projects were suspended, neither statement provides the reason for this suspension.
To verify if the first conclusion relies on unstated assumptions or external knowledge.
3
Evaluate Conclusion II using formal logic against Statement I.
Conclusion II is valid. Using the contrapositive (modus tollens): if the recreational space is less than 15%15\% (e.g., 10%10\%), then the condition of being greater than 50,00050,000 square feet must be false.
To check whether the second conclusion represents a mathematically and logically sound deduction from the given rules.

Anahtar Kavram

Logical Deduction, Modus Tollens, and Distinguishing Inference from Assumption
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Konular

Statement and Conclusions or Inferences

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