Prepositional Phrase As A Complement Or Adverb?

Anonymous am a little confuse about 2 and 3.What is the difference between a complement of a verb and an adverb phrase of a verb?In other words, using the example wiki gives me, what's the difference between deal with the problem and swim in the pool

"You must deal with the problem".

The essential difference between a complement of a verb and an adverbial is that obligatory elements are always complements (they are needed to complete the verb phrase), whereas optional elements may be complements or adverbials. In that example, the PP "with the problem" is essential for this sense of "deal", meaning something like 'cope with' or 'put right'. And if you say "You must deal", the verb has a different sense (such as "deal the cards"). So the PP is obligatory and thus a complement.

"Would you like to swim in the pool"?

This time, the PP "in the pool" is optional; you could simply say "would you like to swim"? without changing the meaning of "swim", or making the sentence ungrammatical. So the PP is optional; it's an adverbial of place, because it defines where the swimming might take place.

AnonymousSimilarly, what is the difference between a complement of an adjective and an adverb phrase of an adjective?

[1] "They were fraught with danger".
[2] "It was dangerous in the extreme".

In [1] the PP "with danger" is an obligatory complement for this sense of the adjective "fraught" - roughly "full of" or "charged". Omitting it would result in a change of meaning of "fraught" to "anxious" or "distressed". Since it's an obligatory element, it must be a complement. In [2] the PP "in the extreme" modifies the adjective "dangerous" It modifies it by delimiting its meaning to that of the PP, i.e. extremely dangerous. It's not obligatory for this sense of "dangerous", and its omission would not render the sentence ungrammatical, and hence not a complement.

By the way, Wiki is not always a good source of information on English grammar. For example, the element "in the extreme" in [2] is not an adverb phrase, but a preposition phrase functioning as a modifier. An adverb phrase is one that's headed by an adverb like "incredibly" in "She is quite incredibly generous", where the adverb phrase "quite incredibly" modifies the adjective "generous".

BillJ