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BDR Exam Trainer - Interactive exercises for database theory and SQL practice.

Total exercises: 33

Functional Dependencies (FD)

Notation: X → Y means "X determines Y" or "if you know X, you know Y"

Example: StudentID → StudentName (each student ID uniquely determines a name)

Closure (X⁺): All attributes that can be determined from X using the given FDs

Normal Forms

1NF (First Normal Form)

✓ All attributes contain only atomic (indivisible) values

✓ No repeating groups or arrays

Example violation: Student(ID, Name, Phones) where Phones = ["123", "456"]

2NF (Second Normal Form)

✓ Must be in 1NF

✓ No partial dependencies (non-key attributes fully depend on the entire primary key)

Example violation: OrderItem(OrderID, ProductID, ProductName, Quantity)

→ ProductName depends only on ProductID, not on the full key (OrderID, ProductID)

3NF (Third Normal Form)

✓ Must be in 2NF

✓ No transitive dependencies (non-key attributes don't depend on other non-key attributes)

Example violation: Employee(ID, DeptID, DeptName)

→ DeptName depends on DeptID (transitive: ID → DeptID → DeptName)

BCNF (Boyce-Codd Normal Form)

✓ Must be in 3NF

✓ For every FD X → Y, X must be a superkey (uniquely identifies all attributes)

Stricter than 3NF: Even key attributes can't have dependencies from non-superkeys

Example violation: CourseSchedule(Student, Course, Instructor)

→ If Instructor → Course (each instructor teaches one course), but Instructor is not a superkey

Normalization Algorithms

Synthesis (3NF Decomposition)

Goal: Decompose into 3NF while preserving dependencies

Steps:

1. Find minimal cover (Fmin) of functional dependencies
2. For each FD in Fmin, create a relation with those attributes
3. If no relation contains a key of original relation, add one
4. Remove redundant relations (subsets of others)

BCNF Decomposition

Goal: Decompose into BCNF (may lose dependency preservation)

Steps:

1. Find a violating FD: X → Y where X is not a superkey
2. Decompose into: R1(X, Y) and R2(R - Y)
3. Repeat for each resulting relation until all are in BCNF

Key Concepts

Candidate Key: Minimal set of attributes that uniquely identifies a tuple

Superkey: Any set of attributes that uniquely identifies a tuple (not necessarily minimal)

Prime Attribute: Part of any candidate key

Minimal Cover (Fmin): Smallest equivalent set of FDs with:

• Single attribute on right side of each FD
• No redundant FDs
• No redundant attributes on left side