"It is ours."
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Yes, in this case (and in all cases where the pronoun comes after the verb "to be") the article before the pronoun is optional
• Q: whose dog is it? A: it is ours = di chi è il cane? è (il) nostro
The difference is Very subtle and IMHO there is no difference in meaning
However, the article slightly changes the meaning of the sentences in the negative form
• Quel cane non è mio = that dog is not mine (maybe I have one or more dogs, or maybe I don't have any).
• Quel cane non è il mio = that dog is not mine (but surely I have, or I have had, a dog)
But in all other cases the article (or an articulated proposition) is mandatory
• my dog is as quiet as yours = il mio cane è tranquillo come il tuo
• my dog is bigger than yours = il mio cane è più grande del tuo
• your car is green, ours is red = la tua auto è verde, la nostra è rossa
if you put the article before the possessive pronouns, it is never wrong (almost never) http://italian.about.com/od/grammar/a/italian-possessive-pronouns.htm
On Windows or Android, if you click on the "Possession" lesson, you can choose from "Practice" or "Tips". Click on "Tips" to see information about the lesson. You will get different information depending on the platform you have chosen. The Microsoft Windows version of Duolingo has a lot more information in the "Tips", however the Android version is more "chatty" with cute graphics which I find assist with remembering the learning message for the lesson.