Fuzzy inference systems, i.e. systems consisting, in principle, of a fuzzy rule base and an inference mechanism, have been widely investigated from different perspectives including their logical correctness. It is not surprising that the logical correctness led mostly to the questions on the preservation of modus ponens. Indeed, whenever such a system processes an input that is equivalent to one of the rule antecedents, it is natural to expect the modus ponens to be preserved and the inferred output to be identical to the respective rule consequent. This leads to the related systems of fuzzy relational equations where the antecedent and consequent fuzzy sets are known values, the inference is represented either by the direct product related to the compositional rule of inference or by the Bandler-Kohout subproduct, and the fuzzy relation that represents the fuzzy rule base is the unknown element in the equations. The most important question is whether such systems are solvable, i.e. whether there even exists a fuzzy relation that models the given fuzzy rule base in such a way that the modus ponens is preserved.