"The books are in the library."
Translation:Τα βιβλία είναι στη βιβλιοθήκη.
The same for την and τη. If the following word begins with a vowel or κ,π,τ,ψ,ξ,γκ,μπ,ντ then the -ν is retained. To remember them easily, they are the consonants of κάποτε ψάξε=search someday, plus all the double consonants.
I'm pretty sure I read in a different thread, that in cases where -ν is not necessary, omitting the -ν is optional, while in the cases where -ν is necessary, it is obligatory to have it. In other words, as I understood it that both 'στη/στην βιλβλιοθήκη' would be correct while 'στη πέτσετα' would be wrong. Or does this only apply to the masculine στον/στο situation?
Good one, troll. When I don't know I keep -ν, as I feel that the mistake wouldn't then be so serious. Some people apply your rule in the masculine forms too. Bad idea, as -ν there must always be retained to keep these forms distinct from the neutral ones.
Τα βιβλία είναι στην βιβλιοθήκη is not accepted as a correct answer here. Can't you choose between στη and στην in this case?