Construct a Hasse diagram for the poset ({1, 2, 3, 4, 6, 8, 12, 24}, |} and answer the following questions: i) Find the maximal elements. ii) Find the minimal elements. iii) Find the greatest element if it exists. iv) Find the least element if it exists. v) Find all upper bounds of {'l, 2, 3}. vi) Find all lower bounds of{1, 2, 3}. vii) Find the least upper bound of {1, 2. 3} if it exists. viii) Find the greatest lower bound of{i. 2, 3} if it exists