Primary Key

A primary key is the attribute / set of attributes by which we can distinctly identify a: 1) Entity 2) Relationship 3) Weak Entity

Entity

• Each entity in an entity set is distinct
• To materialise this distinctness, the primary key is used. No two entities are allowed to have the same primary key

Relationship

• Let $R$ be a relationship involving $n$ entities, $\{E_i{\}}^n$
• The primary key for $R$ is the union of the primary keys of each set in $\{E_i{\}}^n$
• If the relationship set has attributes $\{A_i{\}}^m$ associated with it, then its primary key will also have $\{A_i{\}}^m$ associated with it

Choosing based on cardinality of relationship

• Many-to-Many: The preceding union of primary keys is a minimal superkey, and is chosen as the primary key
• One-to-Many: The primary key of the "Many" side is a minimal superkey and is used as the primary key
• One-to-One: The primary key of either one of the participating entity sets can count as the primary key

Weak Entity

• A weak entity can be discriminated using the foreign key pointing to the identifying entity, on which it relies for existence