Functional Dependency

Context: FIT2094_MOC · $A\to B$: each $A$ value fixes exactly one $B$ value · the determinant–dependent relationship · classified into full/partial/transitive for Normalisation

Quick Revision

• 🎯 Objective: $A\to B$: each $A$ value fixes exactly one $B$ value ➔ the determinant–dependent relationship.
• 📦 Core Components: directional ➔ composite determinant ➔ full/partial/transitive/total.
• ⚡ Key Constraint: partial/transitive FDs signal redundancy that Normalisation removes.

📝 Core

1. The Dependency

• Definition ➔ $A\to B$ iff each $A$ value has exactly one $B$ value; $A$ is the determinant.
• Directional ➔ $\text{orderno}\to \text{orderdate}$ but not the reverse.
• Composite ➔ $(\text{orderno},\text{prodno})\to \text{qtyordered}$ (needs both).

2. FDs Define Keys

• Super key ➔ determines every attribute.
• Candidate key ➔ a minimal such determinant.
• FIT1058 link ➔ an FD is a function on attribute values.

3. Four Kinds (drive Normalisation)

• Full ➔ depends on all of a composite key (2NF requires).
• Partial ➔ depends on part of the key (2NF removes).
• Transitive ➔ non-key → non-key (3NF removes).
• Total (mutual) ➔ $A\to B$ and $B\to A$ (both candidate keys).

⚖️ Core Decision Matrix

Dependency	Determinant	Removed at
full	whole composite key	(2NF requires)
partial	part of key	2NF
transitive	non-key	3NF
total (mutual)	both candidate keys	—

When It Flips: keys are special FDs — a super key determines the whole tuple. "Bad" FDs (non-key determined by part of a key, or by another non-key) signal the redundancy Normalisation removes.

📊 Exam Execution Trace

Manual Execution Trace

Classifying ASSIGNMENT FDs, key $(\text{proj\_num},\text{emp\_num})$:

Step / State	FD	Kind
0 (Init)	—	—
1	$(\text{proj\_num},\text{emp\_num})\to \text{hours}$	full
2	$\text{proj\_num}\to \text{proj\_name}$	partial
3	$\text{job\_class}\to \text{chg\_hour}$	transitive

⚠️ Common Mistakes

• 💡 FDs hold for ALL valid data, not one instance ➔ $A\to B$ is a business rule over every allowed row, not a coincidence in current data.

🧠 Active Recall

Define a functional dependency and explain why it is directional.

• Hint: Single-valued mapping.

Answer

• Short answer: $A\to B$ iff each $A$ value has exactly one $B$ value; $\text{orderno}\to \text{orderdate}$ but not reverse.
• Why: Composite ➔ $(\text{orderno},\text{prodno})\to \text{qtyordered}$ needs both.

Distinguish full, partial, and transitive dependency.

• Hint: Whole key / part / non-key.

Answer

• Short answer: Full = whole composite key; partial = part of key; transitive = non-key → non-key.
• Why: 2NF/3NF ➔ 2NF removes partial, 3NF removes transitive dependencies.