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DBMS → Normalization 19

Which violates 1NF?
Column storing comma-separated multiple phone numbers
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2NF is violated by
Partial dependencies: non-key attribute depends on part of composite PK
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3NF is violated when
Non-key attribute transitively depends on PK through another non-key attribute
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BCNF requires: for every non-trivial FD X→Y
X must be a superkey
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3NF decomposition guarantees
Both lossless join AND dependency preservation
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BCNF decomposition guarantees
Lossless join always but may NOT preserve all dependencies
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4NF eliminates
Multi-valued dependencies (MVDs)
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5NF eliminates
Join dependencies
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Insertion anomaly means
Cannot insert certain data without inserting unrelated data
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Deletion anomaly means
Deleting one row unintentionally destroys other needed information
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Update anomaly means
Updating one fact requires changing multiple rows causing inconsistency risk
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BCNF is preferred over 3NF when
Eliminating ALL FD-based redundancy is the priority (some FDs can be lost)
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Denormalization is performed to
Improve query performance by intentionally adding some redundancy
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When relation has only one candidate key, 3NF and BCNF are
Equivalent (same set of qualifying relations)
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Practical normalization typically stops at
3NF or BCNF (balance between redundancy and performance)
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BCNF violation: R(A,B,C) with AB→C and C→B. C→B violates BCNF because
C+ = {C,B} ≠ {A,B,C} so C is NOT a superkey
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Moving from 2NF to 3NF removes
Transitive dependencies
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2NF ensures non-key attributes depend on
The ENTIRE primary key
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DKNF (Domain-Key Normal Form) is
Theoretical NF where every constraint follows from domain and key constraints
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DBMS → Introduction to DBMS 19

Armstrong's Reflexivity: if Y⊆X then
X→Y
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Armstrong's Augmentation: if X→Y then
XZ→YZ
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Armstrong's Transitivity: if X→Y and Y→Z then
X→Z
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Armstrong's axioms are
Sound and complete
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Attribute closure X+ is computed by
Starting with X and iteratively adding attributes determined by FD set F
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If A+ = all attributes of R(A,B,C,D) then A is
A superkey determining all attributes
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A canonical cover (Fc) is
Minimal equivalent FD set with no redundancy
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A prime attribute is
Part of at least one candidate key
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A non-prime attribute is
NOT part of any candidate key
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Dependency preservation means
Every FD can be verified from decomposed relations without joins
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Union rule from Armstrong: if X→Y and X→Z then
X→YZ
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Decomposition rule: if X→YZ then
X→Y and X→Z
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Trivial FD X→Y means
Y⊆X (B is a subset of A)
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Multi-valued dependency A→→B means
For each A value, B values independent of all other attributes
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Extraneous attribute in FD can be removed without
Changing the overall closure implied by FD set F
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Non-loss decomposition is another term for
Lossless-join decomposition
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A relation with single-attribute PK is automatically in
2NF (no partial dependencies possible without composite key)
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Pseudotransitivity rule: if X→Y and WY→Z then
WX→Z
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StudentName depends on StudentID in PK(StudentID,CourseID). This is what violation?
2NF - partial dependency
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DBMS → Joins 2

Lossless-join decomposition means
Join of decomposed relations gives exactly the original relation without spurious tuples
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Lossless-join condition for R→R1,R2: the condition is
R1∩R2 → R1 OR R1∩R2 → R2 (intersection is superkey in one decomposed relation)
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