Armstrong's axioms are a set of axioms or, more precisely, inference rules used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong in his paper. It means that attribute in dependencies does not change the basic dependencies. This follows directly from the axiom of reflexivity.

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Prerequisite — Functional Dependencies. The term Armstrong axioms refer to the sound and complete set of inference rules or axioms, introduced by William W. Armstrong, that is used to test the logical implication of functional dependencies.

If F is a set of functional dependencies then the closure of F, denoted as , is the set of all functional dependencies logically implied by F. Why armstrong axioms refer to the Sound and Complete? By sound, we mean that given a set of functional dependencies F specified on a relation schema R, any dependency that we can infer from F by using the primry rules of amrmstrong axioms holds in every relation state r of R that satisfies the dependencies in F. By complete, we mean that using primary rules of amrstrong axioms repeatedly to infer dependencies until no more dependencies can be inferred results in the complete set of all possible dependencies that can be inferred from F.

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Please refer Placement for details. Writing code in comment? Please use ide. Prerequisite — Functional Dependencies The term Armstrong axioms refer to the sound and complete set of inference rules or axioms, introduced by William W. Axioms — Axiom of reflexivity — If is a set of attributes and is subset of , then holds.

If then This property is trivial property. Axiom of augmentation — If holds and is attribute set, then also holds. That is adding attributes in dependencies, does not change the basic dependencies. If , then for any. Axiom of transitivity — Same as the transitive rule in algebra, if holds and holds, then also holds. If and , then Secondary Rules — These rules can be derived from the above axioms.

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## Armstrong’s Axioms in Functional Dependency in DBMS

Prerequisite — Functional Dependencies The term Armstrong axioms refers to the sound and complete set of inference rules or axioms, introduced by William W. Armstrong, that is used to test logical implication of functional dependencies. If F is a set of functional dependencies then the closure of F, denoted as , is the set of all functional dependencies logically implied by F. Why armstrong axioms refers to the Sound and Complete?

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## DBMS - Normalization

Functional dependency FD is a set of constraints between two attributes in a relation. Functional dependency says that if two tuples have same values for attributes A1, A2, The left-hand side attributes determine the values of attributes on the right-hand side. Armstrong's Axioms are a set of rules, that when applied repeatedly, generates a closure of functional dependencies. That is adding attributes in dependencies, does not change the basic dependencies.

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## Inference Rule (IR):

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