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Statements: All pens are pencils. Some pencils are erasers. No eraser is a scale. Conclusions: (I) Some pens are erasers. (II) No pencil is a scale.
Only I follows
Only II follows
Both I and II follow
Neither I nor II follows
Neither I nor II follows
Visualize Venn diagrams: If a conclusion is possible in one scenario but fails in another, it is considered false (Does not follow).
Visualize Venn diagrams: If a conclusion is possible in one scenario but fails in another, it is considered false (Does not follow).
Analyze Statement Relationships
All pens are pencils (Pens inside Pencils). Some pencils are erasers (Intersection between Pencils and Erasers). No eraser is a scale (Erasers and Scales are disjoint).
Evaluate Conclusion (I)
Some pens are erasers: The statements do not establish any mandatory connection between pens and erasers. Since a scenario exists where no pens are erasers, (I) does not follow.
Evaluate Conclusion (II)
No pencil is a scale: The statements only forbid erasers from being scales. Some pencils are erasers, but other pencils (those not being erasers) could potentially be scales. Since this is not definitively true, (II) does not follow.
A: Incorrect because Conclusion I is not definitely true; B: Incorrect because Conclusion II is not definitely true; C: Incorrect because neither conclusion is logically guaranteed by the premises.
D is correct because neither conclusion is logically forced by the provided statements, as there are scenarios where both could be false.
In Syllogism, if a relation is not directly stated and can be drawn in multiple ways, any conclusion asserting a definitive link between those subjects is invalid.
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