1. DATABASE DESIGN Functional Dependencies

2. Overview n Functional Dependencies n Normalization –Functional dependencies –Normal forms

3. Functional Dependencies FD n Describes relationship between attributes in a relation. n 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. 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. n Define all the functional dependencies for the employee data-items

4. n Inclusion Rule - Given table, T with heading, HEAD(T) –If X and Y sets of attributes contained in HEAD(T), AND then X Y n 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 FD Rules

5. Armstrong’s Axioms + n Reflexivity: If Y is a subset of X, then X Y n Self-determination: Y Y n Transitivity: If X Y and Y Z, the X Y n Augmentation: If X Y, then XZ YZ n Union: If X Y and X Z, then X YZ n Decomposition: If X YZ, then X Y and X Z n Pseudotransivity: If X Y and WY Z, then XW Z n Accumulation: If X YZ and Z BW, then X YZB

6. Irreducible Sets of FDs n 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)

7. Review Question n 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.