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Statements: All pens are pencils. All pencils are erasers. Conclusion: All pens are erasers.
Only conclusion follows
Neither follows
Both follow
Data inadequate
Only conclusion follows
Apply the transitive property for universal affirmative statements: if all A are B and all B are C, then all A are C.
Apply the transitive property for universal affirmative statements: if all A are B and all B are C, then all A are C.
Analyze Statement 1
Statement 1 states that all pens are pencils, meaning the set of pens is completely contained within the set of pencils.
Analyze Statement 2
Statement 2 states that all pencils are erasers, meaning the set of pencils is completely contained within the set of erasers.
Verify Conclusion
By combining both statements transitively, pens are inside pencils, and pencils are inside erasers, which means all pens are definitely erasers.
B: Incorrect because the conclusion follows validly. C: Incorrect because only a single conclusion is presented in the question. D: Incorrect because the provided statements contain sufficient and definite data to arrive at a conclusion.
A is correct because the transitive property of categorical syllogism directly connects pens to erasers via pencils.
In standard syllogism chains of 'All A are B' and 'All B are C', always extract the shortcut conclusion 'All A are C' instantly without drawing full diagrams.
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