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Difficulty: MediumSyllogism and Categorical Propositions

A maritime regulatory board is classifying vessel registries and operational zones. The official registry guidelines dictate the following rules:

Statements:
1. All icebreaker vessels are reinforced-hull ships.
2. No reinforced-hull ships are shallow-draft boats.
3. Some shallow-draft boats are coastal patrol crafts.

Candidate conclusions:
I. No icebreaker vessels are shallow-draft boats.
II. All reinforced-hull ships are icebreaker vessels.
III. Some icebreaker vessels are reinforced-hull ships.
IV. Some coastal patrol crafts are not reinforced-hull ships.

Which of the given conclusions logically follow(s) from the official guidelines?

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

Answer

Only I and IV follow
Conclusions I and IV are derived through valid syllogistic rules. Conclusion I correctly chains a universal affirmative and a universal negative to form a valid universal negative. Conclusion IV correctly chains a particular affirmative and a universal negative to form a valid particular negative.

Step-by-Step Solution

1
Evaluate Conclusion I using Statements 1 and 2.
Conclusion I is valid.
Statement 1 (All icebreakers are reinforced) and Statement 2 (No reinforced are shallow-draft) logically combine to prove that no icebreakers can be shallow-draft boats.
2
Evaluate Conclusion II based on Statement 1.
Conclusion II is invalid.
The statement 'All icebreaker vessels are reinforced-hull ships' does not mean all reinforced-hull ships are icebreakers. This is an illicit conversion.
3
Evaluate Conclusion III based on Statement 1.
Conclusion III is invalid.
Under strict logical rules, a universal statement ('All icebreakers...') does not guarantee the existence of instances ('Some icebreakers...'). Deriving a particular conclusion solely from a universal premise is an existential fallacy.
4
Evaluate Conclusion IV using Statements 2 and 3.
Conclusion IV is valid.
Statement 3 establishes that some coastal patrol crafts fall into the category of shallow-draft boats. Statement 2 establishes that absolutely no shallow-draft boats are reinforced-hull ships. Therefore, those specific coastal patrol crafts cannot be reinforced-hull ships.

Key Concept

Evaluating valid categorical deductions and avoiding existential fallacies and illicit conversions.
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Topics

Syllogism and Categorical Propositions

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