Read the following four advanced propositions regarding English grammar and syntax, specifically focusing on spotting common errors in complex sentence structures:I. In sentences featuring superlative adjectives modified by emphatic phrases like *'by far'* or *'the very'*, the inclusion of a preceding definite article is syntactically obligatory when the superlative directly precedes a nominal head or functions predicatively within a comparative domain (e.g., *'She is by far the most talented pianist in the orchestra'*, whereas omitting the article yields ungrammaticality in standard registers).II. When two singular nouns modified by distinct determiners are conjoined by coordinate conjunctions to represent two separate, non-overlapping entities (e.g., *'The director and the producer has arrived' *), the governing matrix verb must invariably appear in the singular form to reflect collective conceptual unity.III. In inverted conditional clauses where the subordinating conjunction *'if'* is elided, the auxiliary verb must undergo subject-auxiliary inversion and precede the nominal subject (e.g., *'Had the committee reviewed the proposal earlier, the discrepancy would have been avoided'*), rendering forms without inversion ungrammatical.IV. The correlative conjunction pair *'scarcely... when'* or *'hardly... when'* requires the matrix clause containing *'when'* to be introduced by the simple past tense, whereas the subordinate clause governed by *'scarcely'* must be cast in the past perfect tense with mandatory subject-auxiliary inversion.Identify the option that correctly evaluates the grammatical and syntactic validity of propositions I, II, III, and IV according to standard English grammar and English syntax principles.