For each of the following partially ordered sets, determine which elements are maximum

Chapter 55, Problem 55.2

(choose chapter or problem)

For each of the following partially ordered sets, determine which elements are maximum, maximal, minimum, and minimal. a. The integers f1; 2; 3; 4; 5g ordered by ordinary less than or equal to, . b. The integers f1; 2; 3; 4; 5g ordered by divisibility, j. c. 2 f1;2;3g ; , that is, the set of all subsets of f1; 2; 3g ordered by is-a-subset-of (see Example 54.4). d. Let X D fn 2 Z W n 2g. Let P D .X; j/; that is, P is the poset of all integers that are greater than 1, ordered by divisibility. e. Let X be the set of all people who are currently living. Form a partial order on X with a < b provided a is a descendant of b. (In other words, a is the child, grandchild, or great grandchild, etc. of b.)