Sentence:  However, Coordination facts seem to undermine this hasty conclusion: thus, consider the following:/  (43)      [Your sister could go to College], but ["would she get a degree"?]/  The second (italicised) conjunct is a <WSD>Clause</WSD> containing an inverted Auxiliary, "would". Given our earlier assumptions that inverted Auxiliaries are in C, and that C is a constituent of S-bar, it follows that the italicised <WSD>Clause</WSD> in (43) must be an S-bar. But our familiar constraint on Coordination tells us that only constituents belonging to "the same Category" can be conjoined. Since the second <WSD>Clause</WSD> in (43) is clearly an S-bar, then it follows that the first <WSD>Clause</WSD> must also be an S-bar — one in which the C(omplementiser) position has been left empty. 
Meaning of the word marked with <WSD> tags:  A verb along with its subject and their modifiers. If a clause provides a complete thought on its own, then it is an independent (superordinate) clause; otherwise, it is (subordinate) dependent.