What determines that 책 is supposed to be plural in this sentence? I got "book" marked wrong and the correction said it should be "books"
We would say “a woman or a book”, “the woman or the book” or “women or books”. I cannot think of any situation in which that choice would exist in English in the singular without articles. I mean you could do that with abstract concepts like “This is a situation of life or death.”, but these are concrete things.
I see that a lot of people are getting their answers to questions like these wrong because duolingo is saying the words in the answer are plural when it's teaching that 들 indicates plural. If the answer was "Women or books" it should look like this according to duolingo: 여자들 또는 책들
If the plural is indicated, then you have no choice, but in Korean they often don’t bother to indicate the plural so without the plural character 들, then you have the choice of singular or plural and both are accepted by Duolingo. Some people are not using articles or use an article with only one of the two words. “A woman or a book” and “Women or books” are both accepted as correct and “The woman or the book” should also be accepted as correct. The answer at the top of this page is just one possible answer and at the moment it is “A woman or a book”. If you have the tiles to choose from, there will always be tiles to make at least one possible answer although it may not necessarily be the one that you were thinking of. If you have the multiple choice, then you have to choose all correct answers.