How do I break down the Complement further in accordance with X bar theory.
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I've given what i deem to be a reasonably standard phrase-structure tree for a that-relative clause, consistent with the principles of X-bar theory below (taking Jackendoff, 1977 as a concrete reference). I'm assuming the DP hypothesis here (i.e. that 'a book...' is headed by a determiner rather than by the noun), but it's easy to re-cast this in terms on an NP if that displeases you.
Relative clauses are generally taken in generative syntax to involve wh-movement. Since there is no overt wh-word in a that-relative, this is modelled by positing a null relative operator. Evidence that relative clauses involve wh-movement comes from facts like the following: (i) Relative clauses can be formed using wh-words, as in (1):
(1) A book which i bought.
(ii) Relativisation seems to obey the same constraints as wh-movement, e.g. It can cross a finite clause boundary, as indicated by (2):
(2) A book that Vera said Op_i that John had bought t_i.
(iii) Relativisation is blocked by the presence of a syntactic island. Sensitivity to islandhood is generally taken as being diagnostic of, or even definitional of wh-movement. This can be illustrated by the fact that (2) is ungrammatical, where movement out of a syntactic island - Specifically, a complex subject:
(3) *A book Op_i that a copy of t_i was stolen
Example (4) Shows that wh-movement out of a complex subject leads to ungrammaticality:
(4) *Which book was a copy of t_i stolen?
(iv) There are languages in which an overt realisation of a wh-word alongside that in a relative clause is grammatical, e.g. in Middle English:
(5) thy freend which that thou has lorn (cmctmeli.m3, 218.C1.31) 'your friend that you have lost' (Retrieved from: http://www.ling.upenn.edu/~beatrice/syntax-textbook/ch11.html)