Syllogism — Assess the inference from the given statements: Statements: • All professors are learned. • All learned people are gentle. Inference to test: All professors are gentle persons.
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AThe inference is true.
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BThe inference is false.
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CThe inference is probably true or probably false.
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DThe inference is irrelevant.
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ECannot be determined
Answer
Correct Answer: The inference is true.
Explanation
Introduction / Context:This is a straightforward two-step subset chain. We must decide whether the stated inference is a necessary consequence of the premises.
Given Data / Assumptions:
- All professors are learned.
- All learned people are gentle.
Concept / Approach:If A ⊆ B and B ⊆ C, then A ⊆ C. Here: Professors ⊆ Learned ⊆ Gentle.
Step-by-Step Solution:1) From “All professors are learned,” every professor is in the set Learned.2) From “All learned are gentle,” every member of Learned is in Gentle.3) Therefore every Professor is in Gentle, which is exactly the tested inference.
Verification / Alternative check:Any Venn diagram with concentric containment Learned inside Gentle and Professors inside Learned validates the inference.
Why Other Options Are Wrong:
- “False”: contradicts the transitive inclusion.
- “Probably true/false” or “irrelevant”: this is a deductive certainty, not probabilistic.
Common Pitfalls:Overcomplicating a direct chain; forgetting that two universal inclusions compose into a third.
Final Answer:The inference is true.