Clever students would put a truly complete answer on their homeworks. We shall suppress the dots in subsequent tree-diagrams. Sincere syntacticians might examine the evidence in support of that claim. Tree Diagrams are a means for representing constituent structure.
Categories are groupings of constituents that are alike in various ways.
Tree diagrams that have their component constituents labelled categorially represent Categorial Constituent Structure or Phrase Structure , and are called Phrase Markers . Phrase Markers constitute one representational system. Labelled Bracketings constitute another. All sentences are hierarchically structured, built up from words and phrases. Each part of this structure belongs to a specific category.