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26 September, 02:51

What are Armstrong's Axioms?

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  1. 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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