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DATABASE DESIGN. Functional Dependencies. Overview. Functional Dependencies Normalization Functional dependencies Normal forms. Functional Dependencies FD. Describes relationship between attributes in a relation.

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database design


Functional Dependencies

  • Functional Dependencies
  • Normalization
    • Functional dependencies
    • Normal forms
functional dependencies fd
Functional Dependencies FD
  • Describes relationship between attributes in a relation.
  • If two tuples of a table agree on their X value they also agree on their Y value
  • If A and B are attributes of relation R, B is functionally dependent on A (denoted A B), if each value of A in R is associated with exactly one value of B in R.
  • Define all the functional dependencies for the employee data-items
fd rules
FD Rules
  • Inclusion Rule - Given table, T with heading, HEAD(T)
    • If X and Y sets of attributes contained in HEAD(T), AND then X Y
  • Trivial Dependency - FD of the form X Y that hold for any T where X, Y HEAD(T)
    • example - right hand side subset of left side
armstrong s axioms
Armstrong’s Axioms +
  • Reflexivity: If Y is a subset of X, then X Y
  • Self-determination: Y Y
  • Transitivity: If X Y and Y Z, the X Y
  • Augmentation: If X Y, then XZ YZ
  • Union: If X Y and X Z, then X YZ
  • Decomposition: If X YZ, then X Y and X Z
  • Pseudotransivity: If X Y and WY Z, then XW Z
  • Accumulation: If X YZ and Z BW, then X YZB
irreducible sets of fds
Irreducible Sets of FDs
  • Set, S of FD irreducible iff
    • right-hand side of every FD in S singleton set
    • left-hand side of every FD in S irreducible in turn (no determinant can be discarded from the determinant without loosing information
    • No FD can be discarded from S without changing closure (loosing information)
review question
Review Question
  • Consider the following two sets of functional dependencies_

F = (A C, AC D, E AD, E H)

G = (A CD, E AH)

Check whether they are equivalent.