Present Perfect vs. Past Simple when there is still a chance for the subject to do what they are being asked about

Question

The context: I am looking for a book at home. I can't find it anywhere. I think my roommate could help me.

1. The roommate is still at home. I ask him/her "Have you seen the book?" I think that the form is correct here.
2. The roommate is out (I'm calling him) and I am sure he/she will not come back untill I find the book. Should I say "Did you see the book" or "Have you seen the book?" From what I know about the difference between the Past Simple and the Present Perfect, I should choose the first one.
3. The roommate is out, but there is a high probability that he/she could come back before I find the book. Again, should I say "Did you see the book" or "Have you seen the book?"

Answer 1

You should ask: "Have you seen the book?" because you are looking for it now and you want to know if he knows where it is.

If you ask:"Did you see the book?" you are talking about a past moment, with no relevance to the present.