Define the relation defined as xy whenever x is a factor of y. Let S =...

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Define the relation defined as xy whenever x is a factor of y. Let S = {0, 1, 2, 3, 4, 6, 10, 12, 20}. T = {1, 2, 3, 4, 6, 10, 12, 15, 20) a. Is (S,) a poset. If yes, draw the Hasse diagram. Also, find all the upper bounds and lower bounds as well as the lub and glb for the subset A = {2,3,6,10} of S. b. Is (T,) a poset. If yes, draw the Hasse diagram. Also, find all the upper bounds and lower bounds as well as the lub and glb for the subset A = {2,3,6,10} of T. c. Which of (S, <) and (T, <) are/is lattice(s)? Give reason(s). -----End----- Define the relation defined as xy whenever x is a factor of y. Let S = {0, 1, 2, 3, 4, 6, 10, 12, 20}. T = {1, 2, 3, 4, 6, 10, 12, 15, 20) a. Is (S,) a poset. If yes, draw the Hasse diagram. Also, find all the upper bounds and lower bounds as well as the lub and glb for the subset A = {2,3,6,10} of S. b. Is (T,) a poset. If yes, draw the Hasse diagram. Also, find all the upper bounds and lower bounds as well as the lub and glb for the subset A = {2,3,6,10} of T. c. Which of (S, <) and (T, <) are/is lattice(s)? Give reason(s). -----End-----