Suppose A CR and B CR are sets, and that a = sup A and b = sup B exist. (a) Prove that ANB is bounded above by a (and also by b). (b) Suppose ANB+ 0. Prove that ANB has a supremum, m say, and that m < min{a, b}. (c) If An B+ Ø is it necessarily the case that m = proof or give a counterexample. min{a, b}? Either give a

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