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Difficulty: MediumStatement and Conclusions or Inferences

Consider the following statements and the subsequent conclusions.

Statements:
1. A recent municipal decree mandates that all manufacturing units generating hazardous chemical waste must relocate to the designated special industrial zone outside the city limits by the end of the current year.
2. 'NovaChem' and 'PolyTech' are manufacturing units currently operating well within the city limits.

Conclusions:
I. If NovaChem generates hazardous chemical waste, it is legally required to relocate to the designated special industrial zone by the end of the current year.
II. If PolyTech relocates to the designated special industrial zone by the end of the current year, it implies that PolyTech definitely generates hazardous chemical waste.

Which of the given conclusions logically follows from the statements?

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

Answer

Only conclusion I follows.
Conclusion I is a direct and valid logical deduction (Modus Ponens) from Statement 1. If NovaChem meets the criteria of generating hazardous waste, it is subject to the relocation mandate. Conclusion II, however, does not logically follow. It commits the formal fallacy of affirming the consequent. Statement 1 dictates what hazardous waste generators must do, but it does not state that *only* hazardous waste generators relocate. PolyTech could choose to relocate to the special industrial zone voluntarily for other reasons, such as tax incentives or better infrastructure.

Step-by-Step Solution

1
Analyze Statement 1 to determine the logical condition established.
The decree establishes a one-way conditional rule: IF a unit generates hazardous chemical waste, THEN it must relocate to the special industrial zone.
Understanding the directional nature of conditional statements is required to evaluate logical inferences properly.
2
Evaluate Conclusion I based on the established condition.
Conclusion I applies the premise exactly: If NovaChem meets the 'IF' condition (generates hazardous waste), it faces the 'THEN' outcome (must relocate). This logically follows as a valid deduction.
To test if the conclusion strictly adheres to the stated rule without assumptions.
3
Evaluate Conclusion II based on the established condition.
Conclusion II assumes the reverse: If a unit meets the 'THEN' outcome (relocates), it must satisfy the 'IF' condition (generates hazardous waste). This does not logically follow, as units might relocate for other unstated reasons.
To check for the logical fallacy of affirming the consequent.

Key Concept

Conditional Logic and the Fallacy of Affirming the Consequent
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Topics

Statement and Conclusions or Inferences

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