Properties of RelationalDecompositions (3) Dependency Preservation Property of aDecomposition: Definition: Given a set of dependencies F on R,the projection of F on Ri, denoted by Ri(F) whereRi is a subset of R, is the set of dependenciesX Y in F+ such that the attributes in X υ Y are allcontained in Ri. Hence, the projection of F on each relationschema Ri in the decomposition D is the set offunctional dependencies in F+, the closure of F,such that all their left- and right-hand-sideattributes are in Ri.
Question
Properties of RelationalDecompositions (3) Dependency Preservation Property of aDecomposition: Definition: Given a set of dependencies F on R,the projection of F on Ri, denoted by Ri(F) whereRi is a subset of R, is the set of dependenciesX Y in F+ such that the attributes in X υ Y are allcontained in Ri. Hence, the projection of F on each relationschema Ri in the decomposition D is the set offunctional dependencies in F+, the closure of F,such that all their left- and right-hand-sideattributes are in Ri.
Solution
The Dependency Preservation Property of a Relational Decomposition states that when we decompose a relation into multiple smaller relations, the functional dependencies that hold in the original relation should still hold in the decomposed relations.
To understand this property, let's define some terms. Given a set of dependencies F on relation R, the projection of F on a subset Ri of R, denoted as πRi(F), is the set of dependencies X → Y in F+ (the closure of F) such that all the attributes in X and Y are contained in Ri.
In other words, the projection of F on each relation schema Ri in the decomposition D is the set of functional dependencies in F+ such that all their left-hand and right-hand side attributes are in Ri. This means that the dependencies that hold in the original relation are preserved in each decomposed relation.
By ensuring the dependency preservation property, we can maintain the integrity and consistency of the data when decomposing a relation. It allows us to perform operations on the decomposed relations without losing any important dependencies that were present in the original relation.
Similar Questions
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