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Difficulty: EasySyllogism and Categorical Propositions

Examine the two premises given below:

Premise 1: All engineers are professionals.
Premise 2: No professionals are illiterate.

Now evaluate the following candidate conclusions:
Conclusion I: No engineers are illiterate.
Conclusion II: Some illiterate individuals are engineers.

Which of the following options accurately identifies the logically valid conclusion(s)?

  1. Conclusion I alone is logically validAnswer
  2. B
    Conclusion II alone is logically valid
  3. C
    Both Conclusion I and Conclusion II are logically valid
  4. D
    Neither Conclusion I nor Conclusion II is logically valid

Answer

Conclusion I alone is logically valid.
The correct response identifies that only Conclusion I logically follows. Combining the universal affirmative statement 'All engineers are professionals' with the universal negative statement 'No professionals are illiterate' guarantees that the group of engineers has no intersection with illiterate individuals.

Step-by-Step Solution

1
Analyze the distribution of terms in the premises.
The subject term 'engineers' is fully contained within the middle term 'professionals'. The predicate term 'illiterate' is completely excluded from 'professionals'.
Establishing set relations helps determine validity in standard categorical syllogisms.
2
Evaluate Conclusion I (No engineers are illiterate).
Since the set of 'engineers' is entirely inside 'professionals', and no 'professionals' overlap with 'illiterate', there can be no overlap between 'engineers' and 'illiterate'. Thus, Conclusion I is logically valid.
Universal affirmative combined with universal negative produces a valid universal negative conclusion (EAE-1 figure).
3
Evaluate Conclusion II (Some illiterate individuals are engineers).
Since 'engineers' and 'illiterate' are disjoint sets, any claim asserting an overlap between them is invalid.
An affirmative particular conclusion cannot follow from a valid universal negative relation.

Key Concept

Syllogistic Deduction with Universal Categorical Propositions
Estimated Time:45s
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Topics

Syllogism and Categorical Propositions

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