a. S36 is the set of all divisors of 36 and D is the relation divisor...

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a. S36 is the set of all divisors of 36 and D is the relation "divisor of" on S36, prove that (S36, D) is a complemented lattice. Also draw Hasse diagram for the same. b. Answer these questions for the po-set: ({{1}, {2}, {4}, {1, 2}, {1, 4), (2, 4), (3, 4), (1, 3, 4), (2,3,4}}, ), 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 {{1}, {4}}. f) Find the least upper bound of {{1,2}, {4}}, if it exists. Once you unl JO a. S36 is the set of all divisors of 36 and D is the relation "divisor of" on S36, prove that (S36, D) is a complemented lattice. Also draw Hasse diagram for the same. b. Answer these questions for the po-set: ({{1}, {2}, {4}, {1, 2}, {1, 4), (2, 4), (3, 4), (1, 3, 4), (2,3,4}}, ), 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 {{1}, {4}}. f) Find the least upper bound of {{1,2}, {4}}, if it exists. Once you unl JO