a book to improve your Italian

[azz]

a. I am sending you a book to improve your Italian.

Would you say that sentence corresponds to:
1. I am sending you a book to improve your Italian with. (you are going to improve your Italian using the book)
or
2. I am sending you a book which is to improve your Italian. (the book will improve your Italian)
?

I think one can't tell, but at the end of the day, it doesn't change anything.


1a. I am giving you a pen to sign the papers (with).
2a. I am sending you a repairperson to repair your computer.

However I don't think
2b. I am sending you a repairperson who is to repair your computer.
is natural, although not incorrect...

Many thanks