In advanced English morphosyntax and Determiner Phrase (DP) theory, the distribution, omission, and selection of articles and quantificational determiners are governed by strict semantic, syntactic, and phonological constraints. Consider the following four advanced propositions: I. In coordinate noun phrases where two or more distinct nominal heads refer to separate individuals or distinct entities, the definite article must be repeated before each noun (e.g., 'The chairman and the treasurer have signed the audit report', taking plural verbal agreement), whereas omitting the article before the second noun forces a single-entity or shared-role reading ('The chairman and treasurer has approved the budget'). II. Uncountable mass nouns and plural count nouns universally take the zero article across all syntactic environments, without exception, regardless of whether their reference is generic, universal, specific, or subsequently restricted by post-modifying relative clauses or prepositional phrases. III. Quantifying determiners such as 'few' and 'little' function as inherently negative polar items implying near-absence, insufficiency, or scarcity, whereas their overtly modified counterparts 'a few' and 'a little' carry a positive partitive force denoting a small but sufficient quantity, licensing distinct distributional patterns in existential and conditional environments. IV. The selection between the indefinite articles 'a' and 'an' is strictly determined by the orthographic spelling of the initial letter of the following word in print (e.g., choosing 'an' before any word beginning with a written vowel glyph 'a, e, i, o, u'), completely overriding the acoustic phonological onset or phonetic pronunciation of the word. Identify the option that correctly evaluates the syntactic, semantic, and morphological validity of propositions I, II, III, and IV according to standard English grammar and Determiner principles.