Set Equivalence Theory

Set Equivalence Theory (commonly abbreviated to SET, sometimes redundantly SET Theory) is an advanced sudoku solving technique. It states that if any set of cells 𝐴 is known to contain the same collection of digits as any set of cells 𝐵, then the set difference 𝐴 \ 𝐵 must also contain the same collection of digits as the set difference 𝐵 \ 𝐴. Usually 𝐴 and 𝐵 are chosen to be some union of non-overlapping rows, columns, and 3×3 boxes, meaning that they are known to contain an equal number of every possible digit.