FD Inference Rules

• Definitions

• Examples

Definitions

Reflexivity

If B is a subset of A
then A → B

Augmentation

If B is a subset of A and  C  →  D
then A, C  →  B, D

Transitivity

If A → B  and  B → C
then A → C

Pseudo-transitivity

If A → B and B, C →  D
then A, C → D

Union

If A → B and  → C
then A  →  B, C

Decomposition

If A → B, C
then A → B  and A → C

Self-determination

A → A

[Top]

Examples

Supplier-id, Part-no  →  Qty-on-order

Part-no  →  Qty-on-hand

Supplier-id  →  Supplier-state

Supplier-id, Qty-on-hand  →  Qty-on-hand

is an example of reflexivity

{Qty-on-hand} is a subset of {Supplier-id, Qty-on-hand}

Part-no, Supplier-id  →  Supplier-state

is an example of augmentation

the null set, denoted { } or Ø, is a subset of {Part-no}
Supplier-id   →   Supplier-state

The fact that the FD   Part-no, Supplier-id  →  Supplier-state   can be derived from the given FDs
allows us to say that {Part-no, Supplier-id} is a valid candidate key for CATALOGUE

Account-no  →  Type

Account-no  →  Balance

Type  →  Credit-limit

Account-no  →  Credit-limit

is an example of transitivity

Account-no  →  Type
Type  →  Credit-Limit

The fact that the FD   Account-no  → Credit-limit   can be derived from the given FDs
allows us to say that {Account-no} is a valid candidate key for ACCOUNT

We are given a set of attributes {A, C, T, V} which we put in a relation which we call ACT_FIVE
We ask a friend to specify some FDs

A, C → T
V  → C

A, V  → T

is an example of pseudo-transitivity

V  → C
A, C → T

The derived FD   A, V → T  
allows us to demonstrate that {A, V} is a valid candidate key for ACT_FIVE

a → c

a → t

a → u, p

a → c, t

is an example of union

a  → c
a → t

a → u

a → p

is an example of decomposition

a → u, p

[Top]