Explanation:

Let’s break it down:

- Option 1: "Are these" is totally fine. Standard way to start a question.

- Option 2: "library" is just describing the type of books. No problem here.

- Option 3: "books" is standard and makes sense in the context.

- Option 4: "their" is where things get weird. The sentence is really asking: Do these books belong to them? The word you want is "theirs," not "their" (which is a possessive adjective, not a pronoun).

So—the incorrect segment is Option 4: their.

Option 4 is the right answer.