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Functional Dependencies — Full, Partial & Transitive

When one value always determines another, a functional dependency exists. Learn to read X → Y, classify every dependency by its left side, and see exactly which ones block 2NF and 3NF.

X → Y Full Partial (2NF) Transitive (3NF)

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Section 01

The Story — The Supermarket Barcode

🏷️ REAL-WORLD ANALOGY

One scan, one answer — every time

Scan a barcode at checkout and it instantly reveals the product's name and price. Scan the same barcode again and you get the same result — always. That's a functional dependency: when one value consistently determines another, barcode → (name, price).

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The Notation & the Test

In X → Y, X is the determinant and Y the dependent. The test: if any two rows share the same X but differ on Y, the dependency fails.

Section 02

The Vocabulary You Need

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Prime attribute

Belongs to at least one candidate key — e.g. Order_ID, Item_ID in an order-line table.

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Non-prime attribute

Belongs to no candidate key — the descriptive columns like Qty, Item_Name, Dept_Location.

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Trivial vs Non-Trivial

Trivial: Y ⊆ X (like {A,B}→A). Non-trivial: Y not inside X — these are what normalization cares about.

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Everything Starts Here

Every FD type is defined in terms of prime vs non-prime attributes — identify them correctly first, and classification becomes automatic.

Section 04

Two Example Relations

ORDER_ITEM · PK {Order_ID, Item_ID}

Order	Item	Qty	Item_Name
O1	P1	2	Pen
O1	P2	5	Notebook
O2	P1	3	Pen

Composite key → can host partial dependencies.

EMPLOYEE · PK {Emp_ID}

Emp	EName	Dept	Dept_Loc
E1	Raj	D1	Block A
E2	Sara	D2	Block B
E3	Amit	D1	Block A

Single key → can host transitive dependencies.

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Spot the Redundancy

"Pen" repeats for every order of P1; "Block A" repeats for every D1 employee. Those repeats are exactly what partial and transitive dependencies cause.

Section 03

Classify Any Dependency — The Flowchart

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The One-Question Shortcut

Just ask "what's on the left side?" — a whole key → full; part of a key → partial; a non-key attribute → transitive.

Section 05

Full Functional Dependency ✓

A non-prime attribute depends on the entire composite key — remove any part and the determination breaks.

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Neither Half Alone Is Enough

Order_ID alone can't fix Qty (O1 has 2 and 5). Item_ID alone can't either (P1 has 2 and 3). Only the full pair {Order_ID, Item_ID} → Qty works — exactly what 2NF wants.

Section 06

Partial Functional Dependency — Breaks 2NF

A non-prime attribute depends on only part of a composite key. Only possible when the key has multiple attributes.

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Redundancy That Violates 2NF

Item_ID → Item_Name: P1 is always "Pen" regardless of the order. Item_Name depends on half the key, so "Pen" is repeated on every matching row — a partial dependency that breaks 2NF.

Section 07

Transitive Functional Dependency — Breaks 3NF

A non-prime attribute depends on another non-prime attribute through a middle step. "To find Raj's location, first find his department; the department gives the location."

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Non-Key → Non-Key = 3NF Trouble

Emp_ID → Dept_ID → Dept_Location. The location exists because of the department, not the employee — so "Block A" repeats for every D1 employee. A transitive dependency that breaks 3NF.

Section 08

Impact on Normalization

Dependency	Problem	Blocks
Full	None — desirable	—
Partial	Part-key data repeated	2NF
Transitive	Non-key data repeated via a middle attribute	3NF

Section 09

Quick Classification Drills

Dependency	Type	Why	Status
{Order_ID, Item_ID} → Qty	Full	whole composite key	✅ Healthy
Item_ID → Item_Name	Partial	part of composite key	Breaks 2NF
Emp_ID → Dept_Location	Transitive	non-key via another non-key	Breaks 3NF
{Emp_ID, Date} → Emp_ID	Trivial	dependent is inside determinant	Ignore

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Read the Left Side First

Whole key → full · part of a key → partial · a non-key attribute → transitive · dependent already inside → trivial. One glance at the determinant usually settles it.

Section 10

Full vs Partial vs Transitive

Feature	Full	Partial	Transitive
Left side is	whole key	part of key	non-key attribute
Needs composite key	Yes	Yes	No
Goes via a middle attr	No	No	Yes
Desirable?	Yes	No	No
Blocks	—	2NF	3NF
Example	{O,Item}→Qty	Item→Item_Name	Emp→Dept_Loc

Section 11

Three Common Mistakes

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Partial on a single key

Partial dependencies need a composite key. A single-attribute key has no "part" — it's automatically 2NF-compliant.

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Key-to-key called transitive

Transitive means non-key → non-key. If the middle attribute is itself a candidate key, it's not the 3NF-breaking kind.

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Proving FDs from sample rows

Sample rows can disprove a dependency but never prove one. FDs come from business rules, not snapshots.

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Semantics, Not Snapshots

A table that happens to show one name per barcode doesn't prove the FD — only the rule "a barcode always means one product" does. A single counterexample row, however, is enough to kill it.

Section 12

Golden Rules of Functional Dependencies

🏆 NON-NEGOTIABLE RULES

1

Meaning: X → Y means identical X always produces identical Y — one mismatched row disproves it.

2

Classify by the left side: whole key = full, part of key = partial, non-key = transitive.

3

Requirements: partial needs a composite key; transitive needs three or more attributes.

4

Normalization map: remove partial dependencies for 2NF; remove transitive dependencies for 3NF.

5

Prime attributes first: every definition rests on correctly identifying prime vs non-prime attributes.

6

Design goal: full dependencies are the goal — non-prime attributes should depend on the whole key and nothing else.

FINAL

The Foundation of Normalization

X→YThe core notation

FullWhole key · desirable

PartialPart key · breaks 2NF

TransitiveVia non-key · breaks 3NF

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The Foundation Is Set

You can now read X → Y, tell prime from non-prime, and classify any dependency as full, partial or transitive — which is precisely the diagnosis normalization acts on. Next up: Normalization (1NF → 2NF → 3NF → BCNF), where partial dependencies are split out for 2NF and transitive ones for 3NF.

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One Sentence to Remember

Read the left side: whole key is full (good), part of a key is partial (breaks 2NF), a non-key chaining to another non-key is transitive (breaks 3NF).

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