Universal Statement — Libraries and Books “Every library has books.” Which conclusion is fully justified?

Introduction / Context:
This tests conversion of a universal affirmative into an equivalent negative form. “Every library has books” can be re-expressed to emphasize impossibility of a library lacking books.

Given Data / Assumptions:

• Premise: For all x, if x is a library, then x has books.
• We must choose a conclusion that is logically equivalent or directly entailed.

Concept / Approach:
The contrapositive-style rephrasing for set membership: No library is without books. This preserves the universal claim without adding extraneous conditions about purpose or exclusivity.

Step-by-Step Solution:

Verification / Alternative check:
Check other options for overreach: “books are only in library” would imply exclusivity (books do not exist elsewhere), which is not stated. “Libraries are meant for books only” asserts purpose and excludes readers, media, or services—also not stated. “Some libraries do not have readers” is unrelated and not entailed.

Why Other Options Are Wrong:

• Only-in-library or meant-only-for-books: add exclusivity or purpose not present.
• Some libraries do not have readers: independent claim, not deducible.

Common Pitfalls:
Turning a universal inclusion into an exclusivity claim or importing purposes/uses beyond the given predicate.

Final Answer:
No library is without books.