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Question

Difficulty: MediumSyllogism and Categorical Propositions

Read the given statements and candidate conclusions carefully. Assuming the statements to be true even if they seem at variance from commonly known facts, select which of the conclusions logically follow(s) from the given statements.

Statements:
1. All deep-sea submersibles are pressure-resistant vessels.
2. No pressure-resistant vessels are surface dinghies.

Conclusions:
I. No deep-sea submersibles are surface dinghies.
II. Some deep-sea submersibles are surface dinghies.

  1. Only conclusion I followsAnswer
  2. B
    Only conclusion II follows
  3. C
    Either conclusion I or conclusion II follows
  4. D
    Neither conclusion I nor conclusion II follows

Answer

Only conclusion I follows
The correct answer is that only conclusion I follows. The first premise establishes that every deep-sea submersible is inside the category of pressure-resistant vessels. The second premise establishes that no pressure-resistant vessel can be a surface dinghy. Consequently, deep-sea submersibles can never overlap with surface dinghies, making conclusion I ('No deep-sea submersibles are surface dinghies') logically valid.

Step-by-Step Solution

1
Analyze Premise 1
Deep-sea submersibles is a proper subset of Pressure-resistant vessels (A⊆BA \subseteq B).
Universal affirmative statement ('All A are B').
2
Analyze Premise 2
Pressure-resistant vessels and Surface dinghies are disjoint sets (B∩C=∅B \cap C = \emptyset).
Universal negative statement ('No B are C').
3
Combine premises to test Conclusion I
Since A⊆BA \subseteq B and B∩C=∅B \cap C = \emptyset, it logically follows that A∩C=∅A \cap C = \emptyset ('No deep-sea submersibles are surface dinghies').
Transitive property of disjoint set containment.
4
Evaluate Conclusion II
Conclusion II states A∩C≠∅A \cap C \neq \emptyset, which directly violates A∩C=∅A \cap C = \emptyset.
A particular affirmative conclusion cannot hold when the intersection is proven to be empty.

Key Concept

Syllogistic Categorical Deductions (Universal Negative Rule)
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Topics

Syllogism and Categorical Propositions

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