The four main purposes an author has for writing are to entertain, to express personal thoughts, to persuade, and to
A. expose something
B. explain something
C. become famous
D. gather information

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).

hasty generalization