conjunctions - Analysis (tree diagram) of "She hugged and kissed her mother"


I was wondering how linguists analyze sentences like "She hugged and kissed her mother" or "Will you have that with or without syrup?" or "Four and five are the square roots of sixteen and twenty-five, respectively"?


My previous understanding was that all sentences can be analyzed as a tree, with each word being part of the "argument" of exactly one other word. So in the sentence "Will you have that with syrup", will have is the verb that the entire sentence hangs from, with you being the subject, that the object, and with syrup a prepositional phrase in which syrup depends on with. (Please correct me if my understanding is incorrect.) But how would you ever draw a tree for "with or without syrup"? Specifically, whose child is syrup?


My first thought was that with or without forms a sort of super-preposition. But then what about "She rescued and provided shelter for the cat", in which the cat is simultaneously the object of a verb and a prepositional phrase?




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