Is the XML declaration node mandatory?

I had a discussion with a colleague of mine about the XML declaration node (I'm talking about this => <?xml version="1.0" encoding="UTF-8"?>).

I believe that for something to be called "valid XML", it requires a XML declaration node.

My colleague states that the XML declaration node is optionnal, since the default encoding is UTF-8 and the version is always 1.0. This make sense, but what does the standard says ?

In short, given the following file:

<books>
  <book id="1"><title>Title</title></book>
</book>

Can we say that:

1. It is valid XML ?
2. It is a valid XML node ?
3. It is a valid XML document ?

Thank you very much.