六、Determine whether the poset (Partially Ordered Set) (S, ⊆) is alattice where ? ={∅, {1}, {2}, {4}, {1,2}, {1,4}, {3,4}, {1,2,4},{2,3,4}, {1,2,3,4}}Please draw its Hasse diagram and explain your answer. (10%)

(2) Consider the complete bipartite graphKm,n , where the vertex set is partitioned into two disjoint sets V1 and V2with |V1 | = m and |V2 | = n. Derive the necessary and sufficient conditions for ? and ? such that Km，n contains an Eulerian path but NO Eulerian circuit. (Consider all possible cases for m and n ). (10%)

六、Determine whether the poset (Partially Ordered Set) (S, ⊆) is a
lattice where ? ={∅, {1}, {2}, {4}, {1,2}, {1,4}, {3,4}, {1,2,4},{2,3,4}, {1,2,3,4}}

Please draw its Hasse diagram and explain your answer. (10%)

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