Armstrong's Axioms Rules

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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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