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== Properties and axiomatization of functional dependencies ==
{{Main article|Armstrong's axioms}}
Given that ''X'', ''Y'', and ''Z'' are sets of attributes in a relation ''R'', one can derive several properties of functional dependencies. Among the most important are the following, usually called [[Armstrong's axioms]]:<ref name="SilberschatzKorth2010a">{{cite book|author1-link=Abraham Silberschatz|author2-link=Henry F. Korth|author1=Abraham Silberschatz|author2=Henry Korth|author3=S. Sudarshan|title=[[Database System Concepts]]|year=2010|publisher=McGraw-Hill|isbn=978-0-07-352332-3|edition=6th|page=339}}</ref>
* '''Reflexivity''': If ''Y'' is a subset of ''X'', then ''X'' → ''Y''
* '''Augmentation''': If ''X'' → ''Y'', then ''XZ'' → ''YZ''
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