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Question

Difficulty: MediumSyllogism and Categorical Propositions

Below are three premises followed by three candidate conclusions. You must assume the premises to be absolutely true, disregarding any commonly known facts, and determine which of the conclusions logically follows beyond reasonable doubt.

Premises:
1. All velvet drapes are woven fabrics.
2. No woven fabrics are metallic shields.
3. Some metallic shields are heavy armors.

Conclusions:
I. No velvet drapes are metallic shields.
II. Some heavy armors are not woven fabrics.
III. Some woven fabrics are not heavy armors.

Which of the given conclusions strictly follows from the premises?

  1. Only conclusions I and II followAnswer
  2. B
    Only conclusions I and III follow
  3. C
    Only conclusion I follows
  4. D
    All conclusions I, II, and III follow

Answer

Only conclusions I and II logically follow from the premises.
The correct answer accurately identifies that Conclusion I is a valid universal negative chain, and Conclusion II is a valid particular negative derived from the overlap between metallic shields and heavy armors. It correctly rejects Conclusion III because the relationship between woven fabrics and heavy armors is completely undefined in that direction.

Step-by-Step Solution

1
Analyze Premise 1 and 2 to evaluate Conclusion I.
Since all velvet drapes are woven fabrics, and no woven fabrics are metallic shields, velvet drapes can never be metallic shields.
This validates Conclusion I based on universal negative deduction.
2
Analyze Premise 2 and 3 to evaluate Conclusion II.
Some metallic shields are heavy armors. Because no metallic shields are woven fabrics, those specific heavy armors that are metallic shields cannot be woven fabrics.
This validates Conclusion II based on particular negative deduction.
3
Evaluate Conclusion III using the boundaries of the premises.
The premises do not restrict woven fabrics from being heavy armors. It is entirely possible for all woven fabrics to be heavy armors while still maintaining no overlap with metallic shields.
This invalidates Conclusion III, as it cannot be concluded with absolute certainty.

Key Concept

Logical deductions using universal affirmative, universal negative, and particular affirmative premises.
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Topics

Syllogism and Categorical Propositions

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