Statements: Some pens are pencils. Some pencils are erasers. Some erasers are…
2025
Statements:
Some pens are pencils. Some pencils are erasers. Some erasers are sharpeners. Some sharpeners are dusters.
Conclusions:
I. Some sharpeners are not pencils.
II. All dusters are pens.
- A.
only 1st follows
- B.
only 2nd follows
- C.
either 1st or 2nd
- D.
neither 1st nor 2nd
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Show answer & explanation
Correct answer: D
Answer: Neither conclusion follows.
Explanation: All premises are particular ('Some ...') statements, so they only assert existence of overlaps and do not allow definite universal conclusions. We give models that satisfy all premises but make each conclusion false.
To show the first conclusion (Some sharpeners are not pencils) is not definite: consider one object 'a' that is simultaneously a pen, a pencil, an eraser, a sharpener and a duster. This single-object model satisfies every premise (each "Some ..." holds because 'a' lies in the intersection), yet every sharpener (namely 'a') is a pencil, so the statement "Some sharpeners are not pencils" is false in this model.
To show the second conclusion (All dusters are pens) is not definite: keep the object 'a' as above to satisfy the premises, and introduce another object 'b' that is a sharpener and a duster but not a pen. The premises remain true because 'a' provides the required 'Some' overlaps, but 'b' is a duster that is not a pen, so "All dusters are pens" is false in this model.
Since each conclusion can be false in a scenario that still satisfies all premises, neither conclusion follows.