"A woman has her own bag."
Translation:Una donna ha la propria borsa.
My Italian partner tells me that Duolingo is actually a bit misleading here with the meaning of "propria".
It does directly translate as "their own" but more accurately means their own in terms of "it was produced by them".
An easy example she gave me was "la mucca ha la propria latte" - The cow has it's own milk. It's not that the cow is in possession of the milk that gives it the ownership, but the fact it made it.
Hope this clears it up and I hope Duolingo doesn't use it in a misleading way too much.
I wrote "una donna ha la sua propria borsa" which got an Oops, that's wrong. Consider the following. 1. In Chapter 35 of the first great Italian novel, I Promessi Sposi (The Betrothed), Manzoni writes "m'ha detto prima, lui, con la sua propria bocca" (= with his own lips). But although Manzoni's novel is still taught in Italian schools, he was writing in the first half of the 19th century; so, maybe the language has changed. So, let's turn to a contemporary authority. 2. In Maiden & Robustelli's "A Reference Grammar of Modern Italian" published in 2000, Ch. 10 Sect. 11: "Proprio may also be preceded by a possessive adjective indicating person and number of the possessor; this is usually the case with first and second person possessor: Volevo il mio proprio letto. 'I wanted my own bed.' Ma avete abbandonato il vostro proprio giardino. 'But you've abandoned your own garden.'" But the sentence we were asked to translate has a 3rd person possessor. So, it would be unusual to include "sua". And you don't want duolingo teaching you Italian which is either out of date or unusual. So, my sentence was wrong.
In the multiple choice exercise "la propria" and "la sua" are both shown as correct answers, I don't think that is correct, because these will be two different sentences both in english and italian: a woman has her bag, and a woman has her own bag; una donna ha la sua borsa, and una donna ha la propria borsa.