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Statements: All pens are pencils. Some pencils are erasers. Conclusion: I. Some pens are erasers. II. No pen is an eraser.
Only I follows
Only II follows
Either I or II follows
Neither I nor II follows
Either I or II follows
Check for a complementary pair (Some + No) with identical subjects and predicates where both conclusions individually fail to be definitively true.
Check for a complementary pair (Some + No) with identical subjects and predicates where both conclusions individually fail to be definitively true.
Analyze the Statements
All pens are pencils means the pen circle is entirely inside the pencil circle. Some pencils are erasers means the eraser circle intersects pencils, but it may or may not overlap with pens.
Evaluate Individual Conclusions
Conclusion I (Some pens are erasers) and Conclusion II (No pen is an eraser) are both individually doubtful because one diagram can show an overlap while another can show no overlap.
Apply Either-Or Rule
Conclusions I and II form a complementary pair (Some and No) with the same subject and predicate terms. Since one must always hold true, Either I or II follows.
A: Only I is incorrect because the overlap between pens and erasers is not universally guaranteed. B: Only II is incorrect because pens and erasers can potentially overlap. D: Neither is incorrect because the conditions for a complementary pair are fully satisfied.
C is correct because conclusions I and II form a complementary pair (Some and No) with identical subjects and predicates, and both are individually doubtful.
Always check if doubtful conclusions share the same subject and predicate terms to instantly spot potential Either-Or cases.
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