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Statements: All pens are markers. All markers are erasers. Conclusions: (I) Some erasers are pens. (II) All pens are erasers.
Only conclusion I follows
Only conclusion II follows
Both I and II follow
Neither I nor II follows
Both I and II follow
Apply the rule of inclusion: If All A are B and All B are C, then all A are C, and some C are A.
Apply the rule of inclusion: If All A are B and All B are C, then all A are C, and some C are A.
Visualize the Venn Diagram
Represent pens as a small circle inside the circle of markers. Since all markers are erasers, the circle of markers is inside the larger circle of erasers.
Evaluate Conclusion I
Since all pens are inside the eraser circle, it is logically necessary that some portion of the eraser circle consists of pens. Thus, I follows.
Evaluate Conclusion II
Since the set of pens is entirely contained within the set of markers, and the set of markers is entirely contained within the set of erasers, the set of pens is entirely contained within the set of erasers. Thus, II follows.
A: Incorrect because it ignores that both conclusions are logically valid. B: Incorrect because it excludes the validity of conclusion I. D: Incorrect because both conclusions are directly supported by the subset-superset relationships defined in the statements.
C is correct because both conclusions are logically necessary consequences of the nested set relationships: Pens inside Markers inside Erasers.
In Syllogisms, remember that 'All' implies 'Some'. If all A are B, then automatically some A are B, and some B are A.