Statements:Some books are pens. No pen is pencil.Conclusions: Some pen...
Explanation:
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.
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Statements:Some books are pens. No pen is pencil.Conclusions: Some pen...
Statements:
- Some books are pens.
- No pen is a pencil.
Conclusions:
- Some pens are books.
- Some pencils are books.
- Some books are not pencils.
- All pencils are books.
Explanation:
- The first statement states that there is an overlap between books and pens, but it does not imply that all pens are books.
- The second statement creates a clear distinction between pens and pencils, stating that they have no overlap.
- Conclusion 1 follows logically from the first statement, as some pens could be part of the overlap with books.
- Conclusion 2 is not valid, as there is no connection between pencils and books in the statements.
- Conclusion 3 also follows logically from the first statement, as the overlap between books and pens means that some books cannot be pencils.
- Conclusion 4 is not valid, as the second statement establishes that there is no overlap between pencils and pens/books.
Therefore, the correct answer is option C, as conclusions 1 and 3 logically follow from the statements.