Statements: Some papers are pens. All the pencils are pens. Conclusions: Some…
2023
Statements: Some papers are pens. All the pencils are pens. Conclusions: Some pens are pencils.Some pens are papers.
- A.
Only (1) conclusion follows
- B.
Only (2) conclusion follows
- C.
Either (1) or (2) follows
- D.
Neither (1) nor (2) follows
Attempted by 28 students.
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Correct answer: B
Correct answer: Only "Some pens are papers" follows.
Key reasoning:
From 'Some papers are pens' we know there exists at least one object that is both a paper and a pen. Therefore it is also true to say 'Some pens are papers' (the existential statement is symmetric).
From 'All pencils are pens' we only have a universal inclusion (every pencil, if any, is a pen). A universal statement alone does not guarantee existence of pencils, so we cannot infer the existential statement 'Some pens are pencils'. For example, if there are no pencils, the universal statement remains true while the existential conclusion is false.
Hence only the second conclusion follows; the first does not.