(1) WHAT DOES THE TEXTBOOK SAY?
Complement
Halliday & Matthiessen (2004: 122-3):
A Complement is an element within the Residue that has the potential of being Subject but is not; in other words, it is an element that has the potential for being given the interpersonally elevated status of modal responsibility — something that can be the nub of the argument.
Adjunct
Halliday & Matthiessen (2004: 123):
An Adjunct is an element that has not got the potential of being Subject; that is, it cannot be elevated to the interpersonal status of modal responsibility.
(2) EXAMPLES
(a) Consider the following clause:
Maureen gave David the book.
Q1. Can ‘David’ be raised to Subject?
A. Yes, as follows: David was given the book by Maureen.
Conclusion: ‘David’ is Complement.
Q2. Can ‘the book’ be raised to Subject?
A. Yes, as follows: The book was given to David by Maureen.
Conclusion: ‘the book’ is Complement.
(b) Consider the following clause:
Maureen gave the book to David.
Q1. Can ‘to David’ be raised to Subject?
A. No. *To David was given the book by Maureen.
Conclusion: ‘to David’ is Adjunct.
(c) Consider the following clause:
The book was given to David by Maureen.
Q1. Can ‘to David’ be raised to Subject?
A. No. *To David was given the book by Maureen.
Conclusion: ‘to David’ is Adjunct.
Q2. Can ‘by Maureen’ be raised to Subject?
A. No. *By Maureen gave the book to David.
Conclusion: ‘by Maureen’ is Adjunct.