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Completeness of the
Armstrong’s Axioms
Note that we can deduce that X Y for some set Y by consulting Armstrong’s axioms if and only if Y X+
- X Y F+ Y X+
- Y X+ and suppose that A Y then X A F+ (definition of X+)
- A Y: X A F+
- X Y F+ (union rule)
- X Y F+ Y X+
- X Y F+ and suppose that A Y then X A F+ (decomposition rule)
- A X+ (definition of X+)
- A Y: A X+
- Y X+
Notes:
Introduction
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Presentation
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Example
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