Source: taken from ISI PhD entrance exam questions.
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$\begingroup$ This is hard to understand. The description of AC makes no sense, a set is not an axiom and even the definition of the set is unclear. NBC is not explicitely given at all. Where do preferences come in when everything is about choice rule. Please give complete and firmally precise statements and explain what you have tried yourself. $\endgroup$– Michael GreineckerJan 6 at 8:55
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