Every counterexample to an argument in the Łukasiewicz matrix is also an order counterexample to that same argument, and vice versa.

Every counterexample to an argument in the Łukasiewicz matrix is also an order counterexample to that same argument, but not always vice versa.

Every order counterexample to an argument is also a counterexample to that same argument in the Łukasiewicz matrix, but not always vice versa.

No fuzzy valuation can at the same time be a counterexample to an argument in the Łukasiewicz matrix and also an order counterexample to that same argument.