Functional Dependency in RDBMS

1. FUNCTIONAL
DEPENDENCY
MANASY JAYASURYA
Dept. of Computer Science & Applications
St.Mary’s College, Thrissur

2. CONTENTS
Definition
Functional Dependency Example
Keys
Closure
Axioms
Example
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3. Definition
 A functional dependency is defined as a constraint
between two sets of attributes in a relation from a
database.
Explanation
 Given a relation R, a set of attributes X in R is said to
functionally determine another attribute Y, also in R,
(written X → Y) if and only if each X value is
associated with at most one Y value.
 Here X is the determinant set and Y is the dependent
attribute.
Trivial Dependencies
 Functional Dependency is trivial if and only if right
side is the subset of left side.
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4. Example
Employee
SSNSSN NameName JobTypeJobType DeptNameDeptName
557-78-6587557-78-6587 Lance SmithLance Smith AccountantAccountant SalarySalary
214-45-2398214-45-2398 Lance SmithLance Smith EngineerEngineer ProductProduct
Note: Name is functionally dependent on SSN because
an employee’s name can be uniquely determined from
their SSN. Name does not determine SSN, because
more than one employee can have the same name..
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5. Keys
Key is a set of attributes that uniquely
identifies an entire tuple.
Functional dependency allows to express
constraints that uniquely identify the values of
certain attributes.
However, a candidate key is always a
determinant, but a determinant doesn’t need to
be a key.
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6. Closure
 Let a relation R have some functional
dependencies F specified. The closure of F
(usually written as F+) is the set of all functional
dependencies that may be logically derived from
F. Often F is the set of most obvious and important
functional dependencies and F+, the closure, is the
set of all the functional dependencies including F
and those that can be deduced from F.
 The closure is important and may, needed in
finding one or more candidate keys of the relation.
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7. Axioms for finding Closure of a relation
1. Reflexivity Rule --- If X is a set of attributes and Y is a subset of X, then X
→ Y holds.
2. Augmentation Rule --- If X → Y holds and W is a set of attributes, then
WX → WY holds.
3. Transitivity Rule --- If X → Y and Y → Z holds, then X → Z holds.
Derived Theorems from Axioms
4. Union Rule --- If X → Y and X → Z holds, then X → YZ holds.
5. Decomposition Rule --- If X → YZ holds, then so do X → Y and X → Z.
6. Pseudotransitivity Rule --- If X → Y and WY → Z hold then so does WX
→ Z.
7. Self-determination--- A → A
8. Composition --- If A → B and C → D then AC → BD
9. General Unification Theorem ---
If A → B and C → D , then A U (C-B) → BD 7

8. Example
Student
SNoSNo SNameSName CNoCNo CNameCName AddrAddr Instr.Instr. OfficeOffice
54255425 SusanSusan
RossRoss
102102 Calc ICalc I ……SanSan
Jose,Jose,
CACA
P.P.
SmithSmith
B42B42
RoomRoom
112112
78457845 DaveDave
TurcoTurco
541541 Bio 10Bio 10 ......SanSan
Diego,Diego,
CACA
L.L.
TalipTalip
B24B24
RoomRoom
210210
SNo -> SName CNo -> CName Instr -> Office
SNo -> Addr CNo -> Instr
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9. Back to the Example
SNoSNo SNameSName CNoCNo CNameCName AddrAddr Instr.Instr. OfficeOffice
Based on the rules provided, the following dependencies can be
derived.
(SNo, CNo) →→ SNo (Rule 1) -- subset
(SNo, CNo) →→ CNo (Rule 1)
(SNo, CNo) →→ (SName, CName) (Rule 2) -- augmentation
CNo →→ office (Rule 3) -- transitivity
SNo →→ (SName, address) (Union Rule)
etc.
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10. THANK YOU
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