Answer to Question #15484 in Discrete Mathematics for Sujata Roy

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.