Hello, a Japanese question from me :)

I've just started learning Nihongo and it's going quite smoothly actually, but while doing exercises on 'possessive particles', I mean the "-no" thing, I've encountered something that's not clear for me.



I've caught the basic concept, but my book gives two examples that I'm not quite sure about (I'll be writing in Romaji as I haven't mastered the Japanese keyboard yet ;p):

1) Sore-wa Tanaka-san-no kimono desu-ka? - ok, so we can have situation one: I'm talking with some girl and she's got a kimono that I'm sure I've seen on Tanaka-san (let's say Tanaka's a woman), so I'm asking her if it belongs, by any chance, to Tanaka-san. Or situation two: I'm talking with Tanaka-san and she's wearing an expensive kimono, so I ask her if it belongs to her. That's what the book says.

Everything's clear up to the 2nd example:

2) Are-wa Takashi-san-no daigaku desu-ka? - here the book says that it can only be used when I'm talking with Takashi-san and ask him (let's say that Takashi's a guy) if that uni far away is where he studies. But I guess that we could also imagine such a situation: I'm walking with some Yamada-san and we both know Takashi-san; I see a uni far away and ask Yamada-san if that is the uni Takashi-san said he's at.

Is it me who's mistaken, or is it the book that gives unclear information in this place?