Final answer:
The command 'chmod u=rw file' is used to assign read-write permission exclusively to the owner of a file, and is the correct choice among the given options.
Step-by-step explanation:
The correct command to assign read-write permission to the owner of a file is chmod u=rw file. The chmod command in Unix and Unix-like operating systems is used to change the file's mode bits. The syntax u=rw sets the user's (owner's) permissions to read and write, while file represents the name of the file for which the permissions are being set. Options 1) and 2) modify permissions for all users and only others, respectively, and neither is specific only to the owner.