In each of the following statement and conclusion questions, a pair of statements about books, sharpeners, and erasers is followed by some conclusions. Taking the given statements to be true even if they appear unrealistic, read both conclusions carefully and then decide which of the given conclusions logically follows. Statements: (I) All books are erasers. (II) All sharpeners are books. Conclusions: (I) All sharpeners are erasers. (II) Some books are sharpeners.

Introduction / Context:
This syllogism style question deals with the logical relationships between three sets: books, sharpeners, and erasers. You are given two universal statements and then asked to determine which conclusions must follow. The question tests your ability to chain subset relations correctly and to distinguish guaranteed facts from possibilities.

Given Data / Assumptions:

• Statement (I): All books are erasers.
• Statement (II): All sharpeners are books.
• Conclusion (I): All sharpeners are erasers.
• Conclusion (II): Some books are sharpeners.
• We assume that the statements can be represented by sets and subset relations, with no extra information added.

Concept / Approach:
When one statement says “All A are B” and another says “All B are C,” we can logically combine them to obtain “All A are C.” This is the idea of chaining subsets. However, such universal statements do not automatically guarantee the existence of any elements unless there is a “some” type statement. Therefore, it is important to treat conclusions about existence, such as “some books are sharpeners,” with extra care. A conclusion follows only if it is true in every possible diagram that satisfies the given statements.

Step-by-Step Solution:
Step 1: Represent erasers as a large set.Step 2: Place the books set completely inside the erasers set, because all books are erasers.Step 3: Place the sharpeners set completely inside the books set, because all sharpeners are books. As a result, sharpeners are automatically inside the erasers set as well.Step 4: Analyse conclusion (I): “All sharpeners are erasers.” Since sharpeners lie inside books and books lie inside erasers, every sharpener must also be an eraser. This is a direct consequence of the chain sharpeners subset books subset erasers, so conclusion (I) definitely follows.Step 5: Analyse conclusion (II): “Some books are sharpeners.” This statement asserts the existence of at least one object that is both a book and a sharpener. But the original statements never say that there is at least one sharpener, nor that there is at least one book. It is logically possible, though unrealistic, that there are no books and no sharpeners at all. In that empty model, the statements “All books are erasers” and “All sharpeners are books” still hold, while conclusion (II) fails. Therefore conclusion (II) does not logically follow.

Verification / Alternative check:
To verify, use symbolic reasoning. From statement (II), sharpener implies book. From statement (I), book implies eraser. Combining them, sharpener implies eraser, which is exactly what conclusion (I) says. So conclusion (I) is correct in every scenario. However, the statements never include the word “some,” so they do not guarantee the presence of any actual sharpeners or books. A universal statement like “All sharpeners are books” is logically true even if there are no sharpeners at all. Because of this, the existence claim in conclusion (II) is not ensured.

Why Other Options Are Wrong:
Option B claims that only conclusion (II) follows, which contradicts the direct deduction that sharpeners must be erasers. Option C says that both conclusions follow, but we have shown that conclusion (II) might fail in a valid interpretation. Option D suggests that neither conclusion follows, which ignores the clear chain from sharpeners to erasers. Only option A, which asserts that only conclusion (I) follows, is consistent with proper logical analysis.

Common Pitfalls:
Many students assume that “All sharpeners are books” implies there is at least one sharpener, but in pure logic that is not required. Another common mistake is to forget that once a set is contained inside another, any further container also contains it. Here, because books are inside erasers, and sharpeners are inside books, sharpeners are automatically inside erasers. Careful diagram drawing and awareness of existence assumptions help avoid these errors.

Final Answer:
Therefore, the correct conclusion is that only conclusion (I) follows from the given statements.