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Adam Frye
Computers & Technology
26 September, 02:51
What are Armstrong's Axioms?
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Emmanuel Stanley
26 September, 03:15
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Armstrong's Axioms:
1. - Axiom of reflexivity
2. - Axiom of augmentation
3. - Axiom of transitivity
From these three axioms, the following are derived:
- Proyectivity or union
- Additivity or decomposition
- Pseudotransitivity
Explanation:
Be X, Y, W, Z are sets, then
1. - Axiom of reflexivity : ∀ Y ⊆ X ⇒ X → Y
2. - Axiom of augmentation : X →Y ⇒ ZX → ZY
3. - Axiom of transitivity: X → Y and Y → Z ⇒ X → Z
- Proyectivity or union: X → Y and X → Z ⇒ X → YZ
- Additivity or decomposition: X → Y and Z ⊆ Y ⇒ X → Z
- Pseudotransitivity: X → Y and WY → Z ⇒ WX → Z
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