Relational Database Model

Armstrong's Axioms Rules

FD1 - Reflexivity Rule

If Y ? X, then X ? Y

FD2 - Augmentation Rule

If Z ? W and X ? Y, then XW ? YZ

FD3 - Transitivity Rule

If X ? Y and Y ? Z, then X ? Z

There are three additional rules that are implied by the above rules.

FD4 - Pseudotransitivity Rule

If X ? Y and YW ? Z, then XW ? Z

FD5 - Union Rule

If X ? Y and X ? Z, then X ? YZ

FD6 - Decomposition Rule

If X ? YZ, then X ? Y and X ? Z

The rules of union and decomposition imply that we can always replace a set of functional dependencies with an equivalent set that has only functional dependencies of the form X ? A (i.e., the right-hand side contains a single attribute).

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