Most of the topics covered centers around the concept of using “functional dependency” in analyzing data for information preservation, minimal dedundancy, and for reducing modification anomolies. The context of this discussion is a top-down (analysys) approach to relation designing. Continuing with approach this week, our author(s), using the theory of normal forms and functional dependency, presents a further set of topics related to inferring new functional dependencies from a given data set; notations are discussed including closure, cover, minimal cover, and equivalence. Second, the desirable properties of nonadditive (lossless) joins and preservation of functtional dependencies is discussed. A general algorithm to test for non additivity of joins among a set of relations is presented. This chapter then closes with a discussion of multiple topics specific to the bottom-up (synthesis) approach to database designs.