"These are private books."
Translation:Das sind private Bücher.
From what I believe, here there is no definite defined article. Due to the 'Das sind' structure, not then requiring an 'a' or 'the' to follow it. 'Das ist' would follow a mixed or weak inflection scenario.
As it is 'Das Sind' we then work with the Strong Inflection, and thus: Nominative Plural is -e.
Strong Inflections for nominative are
-er, -e, -es, -e
Masc, Fem, Neu, Plural respectively
You are correct that there is no definite article here (i.e. no "the"). Das in das sind means those (or these, etc). Das in das ist works the same, except it's singular instead.
Since it is just "private books" and not "the private books" or similar, the strong inflection is used. (This is regardless of whether it's das sind or das ist.)
Don't scratch your heads, -analyses:
Diese sind private Bücher. DUO means it is right, but its not!!!
Das sind private Bücher. DUO means it is right, but its not!!!
Dieses sind private Bücher. DUO means it is wrong, but its not!!!
Hence correct answer: "Dieses sind private Bücher."
The owl had a bad day I guess. :-(
Is reported now.