Normalization (1NF → BCNF)

Normalization removes redundancy and update anomalies by decomposing tables based on functional dependencies.

Cheat sheet

▸1NF: atomic values, no repeating groups.
▸2NF: 1NF + no partial dependency (non-key attribute depends on whole candidate key).
▸3NF: 2NF + no transitive dependency (non-key → non-key).
▸BCNF: for every FD X → Y, X is a superkey.
▸Anomalies: insertion, deletion, update.
▸Decomposition should be lossless and ideally dependency-preserving.

Form	Rule	Removes
1NF	Atomic columns	Repeating groups
2NF	No partial dependency	Redundancy on composite keys
3NF	No transitive dependency	Non-key → non-key
BCNF	Every determinant is a superkey	Remaining anomalies
4NF	No multi-valued dependency	Independent multi-valued facts

Student(roll, name, dept, hod)
roll → dept, dept → hod   (transitive)
⇒ Student(roll, name, dept) + Dept(dept, hod)   [3NF]

1. Removing partial dependencies gives:

2. R(A,B,C) with A→B, B→C, key A. Highest form?

3. BCNF condition: for every FD X→Y, X is a:

4. A table with a multi-valued column violates:

5. Denormalization mainly improves: