Three statements are given below followed by two conclusions numbered (I) and…
2023
Three statements are given below followed by two conclusions numbered (I) and (II). Assuming that the information given in the statements is true, even if they seem to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements : All books are pencils. Some pens are erasers. All pencils are pens. Conclusions : I. All books are erasers. II. Some pens are books.
- A.
Both the conclusions (I) and (II) follow.
- B.
Neither conclusion (I) nor conclusion (II) follows.
- C.
Only conclusion (I) follows.
- D.
Only conclusion (II) follows.
Attempted by 158 students.
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Correct answer: D
Statements
All books are pencils.
Some pens are erasers.
All pencils are pens.
From (1) and (3):
Books → Pencils → Pens
So All books are pens.
Now evaluate each conclusion:
Conclusion I: All books are erasers.
We know:
Some pens are erasers (Pens ∩ Erasers ≠ Ø)
But this does NOT guarantee that all pens (or all books) fall in erasers.
So we cannot conclude “All books are erasers.”
❌ Conclusion I does NOT follow.
Conclusion II: Some pens are books.
We have:
All books are pencils
All pencils are pens
So every book is definitely a pen.
Meaning:
The set “books” is inside “pens,” so there is at least some overlap.
Therefore:
Some pens are books ⇒ Always true.
✅ Conclusion II follows.