Question #15484

Different partially ordered sets may be represented by the same Hasse diagramif they are
a) same
b) lattices with same order
c) isomorphic
d) order-isomorphic

Expert's answer

a) It is obvious.

b) It can be different lattices, but the same order. For

instance: {1,2,3} and {1,2,3,4}

c) It is the same as order isomorphism

below

d) Order isomorphism means that both posets represent the same object,

but in different notations. Thus Hasse diagrams coincide.

b) It can be different lattices, but the same order. For

instance: {1,2,3} and {1,2,3,4}

c) It is the same as order isomorphism

below

d) Order isomorphism means that both posets represent the same object,

but in different notations. Thus Hasse diagrams coincide.

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