In advanced English lexicology, semantics, and phraseology, lexical items and figurative idioms often exhibit intricate conceptual nuances, fine-grained oppositions, and metaphorical extensions. Consider the following complex propositions:I. The lexeme 'sagacious' is a precise synonym of 'perspicacious', as both descriptors denote an individual who possesses keen mental discernment, acute judgment, and profound wisdom.II. The idiom 'to hit the nail on the head' implies making an exact, highly accurate, or pinpoint observation, making 'to bark up the wrong tree' its direct conceptual counterpart or antonymous context.III. The word 'equivocal' functions as a direct antonym to 'unequivocal' or 'unambiguous', but it is frequently confused with 'lucid', even though the former denotes something open to multiple interpretations, deliberately vague, or suspicious.IV. The idiom 'to throw caution to the wind' signifies behaving with excessive prudence, calculated caution, and meticulous risk aversion, contrasting sharply with its actual semantic meaning of acting recklessly or taking a bold risk.Identify the option that correctly evaluates the semantic, antonymous, and idiomatic validity of propositions I, II, III, and IV according to standard English lexicography.