# Functional Dependency in Database Management System

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,..., An, then those two tuples must have to have same values for attributes B1, B2, ..., Bn. Functional dependency is represented by an arrow sign (→) that is, X→Y, where X functionally determines Y. The left-hand side attributes determine the values of attributes on the right-hand side.

# Armstrong's Axioms

If F is a set of functional dependencies then the closure of F, denoted as F+, is the set of all functional dependencies logically implied by F. Armstrong's Axioms
are a set of rules that, when applied repeatedly, generates a closure of functional dependencies.

Reflexive rule: If alpha is a set of attributes and beta is_subset_of alpha, then alpha holds beta.

Augmentation rule: If a → b holds and y is attribute set, then ay → by also holds. That is adding attributes in dependencies, does not change the basic dependencies.

Transitivity rule: Same as transitive rule in algebra, if a → b holds and b → c holds, then a → c also holds. a → b is called as a functionally that determines b.

## Trivial Functional Dependency

Trivial: If a functional dependency (FD) X → Y holds, where Y is a subset of X, then it is called a trivial FD. Trivial FDs always hold.

Non-trivial: If an FD X → Y holds, where Y is not a subset of X, then it is called a non-trivial FD.

Completely non-trivial: If an FD X → Y holds, where x intersect Y = Φ, it is said to be a completely non-trivial FD.

Codechief is a very fast growing community among programmers and have a reach of around 1 million+ readers globally. Contribution at Codechief is open for all those who have a passion to learn and help others by sharing their knowledge. If you think you have the zeal to learn, start contributing on Codechief contribute. you can also mail your article to [email protected] See your article appearing on the codechief main page and help other code.

We believe that everyone has the right to learn, so we allow both students and professionals to contribute on Codechief.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

A web enthusiastic, self-motivated Full-Stack Web Developer from Dhaka, Bangladesh with experience in developing applications using JavaScript, Laravel & Wordpress specifically. Facebook Github Website