Question

Answer these questions for the poset ({2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72}, |). a) Find the maximal elements. b) Find the minimal elements. c) Is there a greatest element? d) Is there a least element? e) Find all upper bounds of {2, 9}. f ) Find the least upper bound of {2, 9}, if it exists. g) Find all lower bounds of {60, 72}.

Answer 1

Answer:

(a) maximal elements =27,48,60,72

(b) minimal elements =2,9

(c) greatest element =2,9

(d) least element = Does not exist

(e) upper bounds =18,36,72

(f) least upper bound =72

(g) lower bounds =2,4,6,12

(h) greatest lower bound =12