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Difficulty: HardStatement and Conclusions or Inferences

Analyze the official regulatory framework for special economic zones (SEZ) provided below.

1. An industrial district is granted Tier-1 SEZ status if, and only if, it achieves a certified zero-carbon footprint.
2. Every industrial district that achieves a certified zero-carbon footprint automatically receives a 50% reduction in export tariffs.
3. No industrial district situated within a high-density urban boundary can achieve a certified zero-carbon footprint.

Inference I: Any industrial district that receives a 50% reduction in export tariffs has been granted Tier-1 SEZ status.
Inference II: An industrial district situated within a high-density urban boundary cannot be granted Tier-1 SEZ status.

Based on the framework above, which of the following logically follows?

  1. A
    Only Inference I logically follows
  2. B
    Both Inference I and Inference II logically follow
  3. Only Inference II logically followsAnswer
  4. D
    Neither Inference I nor Inference II logically follows

Answer

Only Inference II logically follows
Inference II is a valid mathematical deduction based on combining Statement 3 and Statement 1. If a district is in a high-density boundary, it cannot be zero-carbon (Statement 3). Because Tier-1 SEZ status requires a zero-carbon footprint as an absolute necessity via the 'if and only if' clause (Statement 1), a high-density district is strictly blocked from obtaining Tier-1 status. Inference I is invalid because it assumes the converse of Statement 2; tariff reductions might be granted for other administrative reasons.

Step-by-Step Solution

1
Analyze Inference I against the statements to test for formal validity.
Inference I is invalid.
Statement 2 establishes that a zero-carbon footprint guarantees a tariff reduction (If A, then B). Inference I assumes that a tariff reduction guarantees a zero-carbon footprint (If B, then A). This is a logical fallacy, as districts might receive reductions for other unstated reasons.
2
Analyze Inference II against the statements using deductive logic chains.
Inference II is valid.
Statement 3 states that a high-density location prevents a zero-carbon footprint. Statement 1 states that a zero-carbon footprint is an absolute requirement (if and only if) for Tier-1 SEZ status. Therefore, the lack of a zero-carbon footprint absolutely prevents Tier-1 SEZ status.

Key Concept

Evaluating formal deductions using biconditionals, necessary vs. sufficient conditions, and contrapositive reasoning.
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Topics

Statement and Conclusions or Inferences

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