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Statements: Some pens are erasers. All erasers are sharpeners. Conclusions: (I) Some sharpeners are pens. (II) All sharpeners are erasers.
Only conclusion I follows
Only conclusion II follows
Both conclusions follow
Neither conclusion follows
Only conclusion I follows
For 'Some A are B' and 'All B are C', the overlap between A and C is guaranteed. 'All C are B' is only true if the circles are identical, which is not guaranteed by the statements.
For 'Some A are B' and 'All B are C', the overlap between A and C is guaranteed. 'All C are B' is only true if the circles are identical, which is not guaranteed by the statements.
Analyze Statement 1 & 2
Some pens are erasers implies an overlap between Pen and Eraser. All erasers are sharpeners means the entire Eraser set is inside the Sharpener set.
Evaluate Conclusion I
Since some pens are erasers and all erasers are sharpeners, the pens that are erasers must also be sharpeners. Thus, some sharpeners are definitely pens. Conclusion I follows.
Evaluate Conclusion II
The statement 'All erasers are sharpeners' does not imply the reverse. It is possible to have sharpeners that are not erasers. Thus, 'All sharpeners are erasers' cannot be definitively concluded.
B is wrong because it includes conclusion II which is not necessarily true; C is wrong because II is invalid; D is wrong because I is valid.
A is correct because conclusion I is a logical necessity derived from the intersection of pens with the larger sharpener set, while conclusion II is a reversal that is not guaranteed.
In Syllogisms, always look for the possibility of a larger set containing a smaller set; never assume the reverse direction for 'All' statements (Conversion rule).