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Syllogism with a particular and a universal negative: ‘‘Some books are pens’’ and ‘‘No pen is pencil’’ – decide which universal/particular conclusions about books and pencils follow.

Difficulty: Medium

Correct Answer: Neither I nor II follows

Explanation:

Premises: (1) Some books are pens (Books∩Pens ≠ ∅). (2) No pen is pencil (Pens∩Pencils = ∅). Conclusions: (I) Some books are pencils. (II) No book is pencil.


Concept/Approach
Track only what is forced by the premises. (1) places some books inside the Pens set; (2) excludes all pens from Pencils. This only tells us that those ‘‘some books’’ that are pens are not pencils. It says nothing about all books.
Test Conclusion I
‘‘Some books are pencils’’ contradicts the possibility that the ‘‘books that are pens’’ cannot be pencils and the remaining books might also not be pencils. I does not follow.
Test Conclusion II
‘‘No book is pencil’’ is too strong. Books outside the Pens set could still be pencils; premises do not rule that out. II does not follow.
Common pitfalls
Overgeneralizing from a particular subset (‘‘some books’’) to the entire class of books.
Final Answer
Neither I nor II follows.
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