Set triplets are relatively rare in simple logic but do occur. Set triplets
can raise the rank of logic except along its minor branch.
Set Triplet Defines Rank 0 Region
The logic in this example is almost a swordfish
except it is missing one candidate. The logic is completed by box 5, which makes
a strong link from 1r6c6 to 1r4c5 where it forms set triplet A. By set theory
rules, the logic has 4 sets, 4 linksets and a basic rank of 0. However, the
set-triplet raises the effective rank to 1 everywhere except along its minor
(linkset) branch, which is still rank 0. The branch includes linksets r21 and
r41, which are both rank 0 as indicated by the black highlight (below). This
eliminates candidate 1r4c8.