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.

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.