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Difficulty: EasySyllogism and Categorical Propositions

Consider the following statements and conclusions:

Statements:
1. All apples are fruits.
2. All fruits are healthy.

Conclusions:
I. All apples are healthy.
II. Some healthy things are fruits.

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

  1. A
    Only conclusion I follows
  2. B
    Only conclusion II follows
  3. Both conclusion I and conclusion II followAnswer
  4. D
    Neither conclusion I nor conclusion II follows

Answer

Both conclusion I and conclusion II follow
Both conclusions logically follow from the given premises. Combining 'All apples are fruits' and 'All fruits are healthy' yields 'All apples are healthy' by transitivity. Additionally, 'All fruits are healthy' can be validly converted to 'Some healthy things are fruits'.

Step-by-Step Solution

1
Analyze Statements 1 and 2 transitively.
Since 'All apples are fruits' and 'All fruits are healthy', the set of apples is entirely contained within the set of healthy items. Thus, 'All apples are healthy' (Conclusion I) is valid.
Transitive property of Universal Affirmative (A-type) categorical propositions.
2
Apply categorical conversion to Statement 2.
The universal affirmative statement 'All fruits are healthy' converts validly to the particular affirmative statement 'Some healthy things are fruits' (Conclusion II).
Rule of conversion for A-type propositions (All S are P implies Some P are S).

Key Concept

Categorical Syllogism: Transitivity and Conversion Rules
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Topics

Syllogism and Categorical Propositions

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