Let R be the rectangle shown here, including the edges. LetH be the set of all

Chapter 3, Problem 13

(choose chapter or problem)

Let R be the rectangle shown here, including the edges. LetH be the set of all rectangles whose sides have positivelength, are parallel to the sides of R, and lie within R. H ispartially ordered by set inclusion.(a) Does every subset of H have an upper bound? a least upper bound? (b) Does every subset of H have a largest element? (c) Does every subset of H have a lower bound?(d) Does every subset of H have a smallest element?

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