If some pens are pencils but no pencil is sharpener then (A) Some pencils are…
2020
If some pens are pencils but no pencil is sharpener then (A) Some pencils are pens (B) Some sharpeners are pencils (C) Some pens are not sharpener (D) Some pencils are not pens
- A.
AC
- B.
BC
- C.
AD
- D.
BD
Attempted by 36 students.
Show answer & explanation
Correct answer: A
Given: Some pens are pencils. No pencil is sharpener.
Some pens are pencils (there exists at least one object that is both a pen and a pencil).
No pencil is sharpener (no object is both a pencil and a sharpener).
Inferences:
From "Some pens are pencils" we can conclude "Some pencils are pens" because existence is symmetric: if there is an object that is both a pen and a pencil, that same object is a pencil that is a pen.
Given that no pencil is a sharpener, the pen that is also a pencil cannot be a sharpener. Hence there exists at least one pen that is not a sharpener, so "Some pens are not sharpener" holds.
The statement "Some sharpeners are pencils" cannot be true because it contradicts the premise that no pencil is a sharpener.
The statement "Some pencils are not pens" is not guaranteed by the premises. It might be true in some cases, but it is also possible that every pencil is a pen, so we cannot conclude it necessarily.
Conclusion: The two statements that necessarily follow from the premises are "Some pencils are pens" and "Some pens are not sharpener". Therefore the correct combination is AC.