P' = dual P
The dual of a poset is the poset on the same ground set but with all relations reversed.
i1 : P = divisorPoset 12;
i2 : dual P o2 = Relation Matrix: | 1 0 0 0 0 0 | | 1 1 0 0 0 0 | | 1 0 1 0 0 0 | | 1 1 0 1 0 0 | | 1 1 1 0 1 0 | | 1 1 1 1 1 1 | o2 : Poset
Clearly then, the chain posets and booleanLattices are all self-dual.
i3 : C = chain 5;
i4 : areIsomorphic(C, dual C) o4 = true
i5 : B = booleanLattice 4;
i6 : areIsomorphic(B, dual B) o6 = true