A Key Point on the Equivalence between Functional Dependencies and Logic Algebra

An equivalence between logic algebra and functional dependencies shows that a functional dependency is implied by a set of functional dependencies if and only if its corresponding product term is implied by corresponding logic function. In this paper we shall state and proof a key point ignored for a long time, that is any prime implicate in a corresponding logic function of a set of functional dependencies correspond a simplest functional dependency whose left side has no redundant attributes. Based on the point many problems in theory of functional dependency, such as computing minimum covers, all candidate keys, and closure of any set of attributes can be solved effectively and uniformly. The conclusion can be extended to data dependencies include multivalued dependencies easily.