Question

离散数学中关于格的一道题！高分悬赏！

let T={1,2,3,4,6,12},s={1,2,3,4,12},let "<=" mean the partial order relation of divisibillity on T and on S.
(1)Determine whether the poset(T,<=)is a lattice.
(2)Determine whether the poset(S,<=)is a lattice.
(3)Determine whether the poset(s,<=)is a sublattice of the poset(T,<=).
理由也写，谢谢！

Answer 1

请画出 <T,<= > 和<S,<= > 此两个偏序集的哈斯图，就可以判断两个偏序集中的任何两个顶点都有最小上界和最大下界，因此就判断此两个偏序集为格。