My understanding is that when you take a predicate and specify a subject, it becomes a proposition. Here, I think it was intended that "you" is not the general term for "somebody" but rather the particular person, you (the reader).
I would write your (i) as
i) (p -> q) is false
just to be extra safe that nobody interprets it as
i) (p -> (q is false)) is true
I can give an illustration of why the book's conclusion is right: Say every Monday when you can access the network, you can change your grade, but only on Monday. So accessing the network is not sufficient for changing your grade, meaning (p -> q) is false. But suppose you have access to the network on all days, meaning p is true. Now given all these facts, we cannot conclude whether q is true, because we don't know what day of the week it is.