Question: For each of the following universal assertions about subsets of R, prove it (if true) or give a counterexample (if false) and explain why

For each of the following universal assertions about subsets of R, prove

For each of the following universal assertions about subsets of R, prove it (if true) or give a counterexample (if false) and explain why it is a counterexample. a) Every bounded nonempty open subset of R is an open interval. b) Every closed nonempty subset of R contains its maximum. c) Every bounded closed nonempty subset of R contains its maximum. d) Every nonempty open subset of R is a union of open intervals.

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