Slide 8.9: Table key (Cont.)

Table Key (Cont.)

Definition (Table Key)
Give a table T, with Head(T)=A₁…A_n. A key for the table T, sometimes called a candidate key, is a set of attributes, K=A_i₁…A_{i_k}, with two properties

(Superkey) If u and v are distinct tuples of T, then by designer intention u[K]≠v[K]; that is, there will always exist at least one column, A_{i_m}, in the set of columns K such that u[A_{i_m}]≠v[A_{i_m}].

(Key) No proper subset H of K has the Property 1.

Example (Table Key)
Calculate the keys of T from a given content:

^†Note that this example is to explain the concept of a key, instead of trying to find the keys from a table content.

T
A	B	C	D
a1	b1	c1	d1
a1	b2	c2	d1
a2	b2	c1	d1
a2	b1	c2	d1

|key| = 1: No single attribute can be a key, since in each column we have at least two equal entries.
D ∈ key: (Superkey) No set S of attributes can be a key if it includes D, since D gives no help in distinguishing rows of T.
|key| = 2: (Key) All rows of T are distinguished by each of AB, AC, and BC.
|key| = 3: (Superkey) Must contain AB, AC, or BC.

Primary Key of a Table
A primary key of a table T is the candidate key chosen by the database designer to uniquely identify specific rows of T.