Can also be called Nonadditive. If you decompose a relation into relations and you will guarantee a Lossless-Join if ⋈ = .
Let be a relation schema.
Let be a set of functional dependencies on .
Let and form a decomposition of .
The decomposition is a lossless-join decomposition of R if at least one of the following functional dependencies are in +(where + stands for the closure for every attribute in ):
- ∩ →
- ∩ →
- Let be the relation schema, with , , and attributes.
- Let be the set of functional dependencies.
- Decomposition into and is lossless under because and so .
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