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Difficulty: MediumSyllogism and Categorical Propositions

An economic policy institute has established a classification system for retail products. The following categorical propositions govern this system:

1. All biodegradable plastics are eco-friendly materials.
2. Some eco-friendly materials are premium-priced products.
3. No premium-priced products are mass-market goods.

Evaluate the logical validity of the following derived deductions:
I. Some biodegradable plastics are premium-priced products.
II. All eco-friendly materials are biodegradable plastics.
III. Some eco-friendly materials are not mass-market goods.

Which of the deductions can be definitively concluded from the established propositions?

  1. Only deduction III is validAnswer
  2. B
    Only deductions I and III are valid
  3. C
    Only deductions II and III are valid
  4. D
    None of the deductions are valid

Answer

Only deduction III is valid
Deduction III is the only valid conclusion. Since some eco-friendly materials are premium-priced, and no premium-priced products are mass-market goods, it logically follows that the premium-priced portion of eco-friendly materials cannot possibly be mass-market goods. Therefore, at least some eco-friendly materials are definitively not mass-market goods. Deductions I and II rely on logical fallacies (undistributed middle and invalid conversion, respectively).

Step-by-Step Solution

1
Analyze Deduction I (Some biodegradable plastics are premium-priced products)
Determined to be invalid.
The first premise places biodegradable plastics entirely within the eco-friendly category. The second premise shows some eco-friendly materials are premium-priced. However, there is no guarantee that the specific eco-friendly materials that are premium-priced include the biodegradable plastics. This is the fallacy of the undistributed middle.
2
Analyze Deduction II (All eco-friendly materials are biodegradable plastics)
Determined to be invalid.
This is an invalid conversion of the first premise. Just because all biodegradable plastics belong to the eco-friendly category does not mean that biodegradable plastics are the only eco-friendly materials in existence.
3
Analyze Deduction III (Some eco-friendly materials are not mass-market goods)
Determined to be valid.
Premise 2 establishes that a specific subset of eco-friendly materials exists within the premium-priced category. Premise 3 states that absolutely zero premium-priced products are mass-market goods. Therefore, that specific subset of eco-friendly materials can never be mass-market goods. It logically follows that at least some eco-friendly materials are not mass-market goods.

Key Concept

Evaluating categorical syllogisms using rules of distribution, conversion, and subset intersections.
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Topics

Syllogism and Categorical Propositions

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