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Is the following statement correct: Let % be an arbitrary complete, transitive and convex preference relation on [0,1], then [0,1] has a greatest element? Provide

Is the following statement correct: "Let % be an arbitrary complete, transitive and convex preference relation on [0,1], then [0,1] has a greatest element"? Provide a proof of your argument. [For this question, maximum word limit is 80.]

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