Suppose A, B are nonempty subsets of R that are bounded above. (a) What is the definition of the sup ...

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Suppose A, B are nonempty subsets of R that are bounded above. (a) What is the definition of the supremum sup A of A? (b) Show that sup(A union B) = max{sup A, sup B}. (c) Suppose the intersection of A and B is nonempty. Is it always true that sup(A intersect B) = min{sup A, sup B}? Either give a proof of the identity, or find a counterexample.