Terms & Definitions

Relation (Table): A relation is a subset of $D_1 \times D_2 \times \dots \times D_n$ (Set of ordered tuples $<d_1, d_2, \dots, d_n>$)

• E.g. $D_1$: Name, $D_2$: Age, a tuple would be <Azalea, 20>

Schema: Definition of the relation structure (e.g. Person(Name, Age))

Instance / Tuple: One row / entry in the relation

Attribute: Column

Arity: Number of columns (fields)

Candinality: Number of rows (entries)

Database Schema/Instance: Set of relation schemas/instances.

Superkey: The minimum set of attributes that uniquely identifies a row (e.g. no two person with the same {name, age} can exist in the table)

• $\neg \exists t_1, t_2: (t_1.a_1 = t_2.a_1) \land (t_1.a_2 = t_2.a_2)$
• If {id} is a superkey, then {id, name} is also a superkey
• Notation: Superkeys are underlined

Key: A minimal superkey (subset of a superkey)

Constraints

Key (Integrity) Constraint: No entries with duplicate keys exist in a table

Referential Integrity Constraint: $R_1[x] \sub R_2[y]$

• Foreign Key Constraint: When $y$ is a unique key of $R_2$

Integrity Constraints: General rules expressed using a query (either $R=\empty$ or $R \sub S$)

Operators [Link]