In analogy questions, first decide the relation (synonym, antonym, degree, cause-effect) before comparing with the options.
Step 1: Relationship in the given pair.
"Flimsy" means weak or fragile, while "sturdy" means strong or solid. They are antonyms.
Step 2: Check each option.
- (a) "Prognosis" (prediction of disease outcome) and "diagnosis" (identification of disease) are related terms, but not opposites.
- (b) "Gauche" (awkward, clumsy) and "eloquent" (fluent, expressive) are somewhat contrasting, but not perfect antonyms.
- (c) "Flippant" (casual, unserious) and "earnest" (serious, sincere) are exact opposites, just like flimsy vs. sturdy.
Step 3: Conclusion.
Option (c) best represents the antonym relationship. \[ \Rightarrow \boxed{(c)} \]
A useful check for analogies is to build a bridge sentence that connects the two given words, then see which option's pair fits the same sentence. Here: "Something flimsy has none of the strength that something sturdy has," a pair of direct opposites in quality.
Only option 3 mirrors the same direct-opposite relationship as flimsy and sturdy.
Hence, the correct answer is flippant : earnest.