Question

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

Answer 1

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.