We investigate the inference rules that can be applied to functional and multivalued dependencies that exist in a database relation. Three types of rules are discussed. First, we list the well known rules for functional dependencies. Then we investigate the rules for multivalued dependencies. It is shown that for each rule for functional dependencies the same rule or a similar rule holds for multivalued dependencies. There is, however, one additional rule for multivalued dependencies that has no parallel among the rules for functional dependencies. Finally, we present rules that involve functional and multivalued dependencies together. The main result of the paper is that the rules presented are complete for the family of functional and multivalued dependencies.