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Difficulty: EasySyllogism and Categorical Propositions

Read the given statements and candidate conclusions carefully.

Statements:
1. All organic chemists are laboratory researchers.
2. No laboratory researchers are commercial sales representatives.

Conclusions:
I. No organic chemists are commercial sales representatives.
II. Some commercial sales representatives are organic chemists.

Which of the following options is correct?

  1. Only conclusion I followsAnswer
  2. B
    Only conclusion II follows
  3. C
    Both conclusion I and conclusion II follow
  4. D
    Neither conclusion I nor conclusion II follows

Answer

Only conclusion I follows
The correct answer states that only conclusion I follows. Combining 'All Organic Chemists are Laboratory Researchers' with 'No Laboratory Researchers are Commercial Sales Representatives' logically guarantees that no member of Organic Chemists can be a Commercial Sales Representative (standard Celarent syllogism mood).

Step-by-Step Solution

1
Represent the premises using categorical set notation
Statement 1 implies Organic Chemists ⊆ Laboratory Researchers. Statement 2 implies Laboratory Researchers ∩ Commercial Sales Representatives = ∅.
Establishing set relations allows determination of set inclusion and exclusion.
2
Evaluate Conclusion I (No organic chemists are commercial sales representatives)
Since Organic Chemists are entirely inside Laboratory Researchers, and Laboratory Researchers have zero overlap with Commercial Sales Representatives, Organic Chemists also have zero overlap with Commercial Sales Representatives. Thus, Conclusion I logically follows.
Subsets of mutually disjoint sets are also disjoint from those sets.
3
Evaluate Conclusion II (Some commercial sales representatives are organic chemists)
Since the intersection between Organic Chemists and Commercial Sales Representatives is empty, Conclusion II is false and does not follow.
An affirmative particular conclusion cannot be derived when the two sets are completely disjoint.

Key Concept

Syllogism - Categorical Deduction with Universal Premises (Celarent Figure)
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Topics

Syllogism and Categorical Propositions

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