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In advanced English lexicology, semantics, and phraseology, words often exhibit intricate nuances of meaning, precise synonym-antonym relationships, and metaphorical idiomatic extensions. Consider the following four advanced propositions regarding synonyms, antonyms, and idioms: I. The adjectives 'fastidious' (showing excessive care, meticulous attention to detail, and hypercritical exactness) and 'cursory' (rapidly and superficially performed without paying attention to details) represent true antonymous pairs, whereas 'ephemeral' and 'transitory' function as near-synonyms denoting short-lived existence. II. The idiomatic expression 'to burn the candle at both ends' signifies working excessively hard or exhausting one's physical and mental resources by overworking, whereas 'to rest on one's laurels' denotes becoming complacent and relying entirely on past achievements without striving for further progress. III. The polysemous nouns 'apathy' and 'fervor' serve as close synonyms denoting a lack of interest, enthusiasm, or emotional engagement, and their shared direct antonym is lexicalized by terms such as 'indifference' or 'detachment'. IV. The idiomatic phrase 'to throw down the gauntlet' historically originates from medieval chivalric traditions and means to issue a formal challenge or provoke a confrontation, whereas its exact semantic counterpart 'to take up the gauntlet' means to accept that challenge and enter the contest. Identify the option that correctly evaluates the lexical, semantic, and idiomatic validity of propositions I, II, III, and IV according to standard English vocabulary and Idiom principles.

Detailed Explanation

Let us evaluate each of the four advanced propositions regarding English vocabulary and phraseology: * **Proposition I is CORRECT:** 'Fastidious' (meticulous, extremely attentive to accuracy and detail) and 'cursory' (done with quick superficiality) are direct antonyms. Similarly, 'ephemeral' and 'transitory' are strong near-synonyms sharing the semantic core of brief duration. * **Proposition II is CORRECT:** 'To burn the candle at both ends' accurately describes exhausting one's vitality by overworking, and 'to rest on one's laurels' correctly refers to resting complacently on past successes. * **Proposition III is INCORRECT:** The noun 'apathy' means a lack of interest or enthusiasm, whereas 'fervor' means passionate intensity and emotional warmth; thus, they are antonyms, not synonyms. 'Indifference' is a synonym of apathy, not its antonym. * **Proposition IV is CORRECT:** 'To throw down the gauntlet' means to issue a challenge, and 'to take up the gauntlet' means to accept that challenge, perfectly reflecting their historical medieval origins and figurative usage. For a deeper understanding of figurative expressions and their structural classifications, review the Idiom Wikipedia reference.
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