Problem

For the partially ordered set A = {a, b, c, d, e, f, g, h} with the Hasse diagram below,...

For the partially ordered set A = {a, b, c, d, e, f, g, h} with the Hasse diagram below, find

(a) all upper bounds for the sets {g, h}, {e, h}, {a, h}, {c, f, g}, and {b, f, g, h}.

(b) all lower bounds for the sets {g, h}, {f, h}, {b, c, d}, {c, f, g}, and {a, d}.

(c) the supremum, if it exists, for the sets {g, h}, {g, c}, {e, g, h}, {b, f, g}, and {c, e}.

(d) the infimum, if it exists, for the sets {b, e, f }, {e, g}, {b, c, d}, and {b, f, g}.

(e) the smallest element, if it exists, for the sets {b, c, f }, {e, g}, {b, c, d}, and {b, f, g}.

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Solutions For Problems in Chapter 3.5

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