The well-known inference rules for FDs

? Reflexive rule :

If Y is subset or equal to X then X Y.

► Augmentation rule:

If X Y then XZ YZ.

► Transitive rule:

If {X Y, Y Z} then X Z.

► Decomposition rule :

If X YZ then X Y.

► Union or Additive rule:

If {X Y, X Z} then X YZ.

► Pseudo Transitive rule :

If {X Y, WY Z} then WX Z.

Of these the first three are known as Amstrong Rules. They are sound because it is enough if a set of FDs satisfy these three. They are called complete because using these three rules we can generate the rest all inference rules.