In the sentence 'She placed the book on the shelf with great care', analyze the highlighted phrases and the assertions below:

I.'On the shelf' is a prepositional phrase functioning as an adverbial of place.

II.'With great care' is a prepositional phrase functioning as an adverbial of manner.

III.Both phrases could be syntactically replaced by single adverbs like 'there' and 'carefully' without changing the core grammatical relations.

Mark the option that presents only the correct statements.