Prove or disprove each of the following statements. a. If a poset has a maximum element
Chapter 55, Problem 55.7(choose chapter or problem)
Prove or disprove each of the following statements. a. If a poset has a maximum element, then it must be unique. b. It is possible for a poset to have an element that is both maximum and minimum. c. It is possible for a poset to have an element that is both maximal and minimal but is neither maximum nor minimum. d. If a poset has exactly one maximal element, then it must be a maximum e. If x is a minimal element in a poset and y is a maximal element in a poset, thenx y.f. If x and y are incomparable, then neither is a minimum.g. Distinct (i.e., unequal) maximal elements must be incomparable
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