Question: Let (A, R) be a poset in which the length of a longest (maximal) chain is n 2. Let M be the set of

Let (A, R) be a poset in which the length of a longest (maximal) chain is n ≥ 2. Let M be the set of all maximal elements in (A, R), and let B = A - M. If R' = (B × B) ⋂ R, prove that the length of a longest chain in (B, R') is n - 1.

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