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Read the given statements and conclusions carefully. Statements: All pens are pencils. No pencil is an eraser. Conclusions: (I) Some pencils are pens. (II) No eraser is a pen.
Only conclusion I follows.
Only conclusion II follows.
Both conclusions I and II follow.
Neither I nor II follows.
Both conclusions I and II follow.
In syllogisms, 'All A are B' implies 'Some B are A', and the negative relationship of the parent category (Pencil) automatically restricts all its subsets (Pens).
In syllogisms, 'All A are B' implies 'Some B are A', and the negative relationship of the parent category (Pencil) automatically restricts all its subsets (Pens).
Analyze Statement 1
All pens are pencils means the set of pens is a subset of the set of pencils. By basic conversion, if all pens are pencils, then some pencils must be pens (Conclusion I follows).
Analyze Statement 2
No pencil is an eraser means the set of pencils and the set of erasers are disjoint. Since pens are entirely contained within pencils, pens are also disjoint from erasers (Conclusion II follows).
A: Incorrect because it ignores the validity of Conclusion II. B: Incorrect because it ignores the validity of Conclusion I. D: Incorrect because both conclusions are logically derived from the given statements.
C is correct because the deduction confirms that some pencils must be pens and the total separation between pencils and erasers necessitates no intersection between pens and erasers.
When dealing with negative syllogisms, always identify the 'container' set first; if the container is blocked from an external group, all subsets inside are blocked too.