Let P D .X; / be a finite poset that is not a total order. Prove that P contains

Chapter 57, Problem 57.4

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Let P D .X; / be a finite poset that is not a total order. Prove that P contains incomparable elements x and y such that 0 D [ f.x; y/g is a partial order relation. Such a pair of elements is called a critical pair.

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