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Chapter 3 The Relational Model

Review Questions

3.1 Discuss each of the following concepts in the context of the relational data model:

(a) Relation (b) Attribute (c) Domain (d) Tuple (e) Intension and Extension (f) Degree and Cardinality.

Each term defined in Section 3.2.1.

3.2 Describe the relationship between mathematical relations and relations in the relational data model?

Let D1, D2, . . . , Dn be n sets. Their Cartesian product is defined as:
D1  D2  . . .  Dn  {(d1, d2, . . . , dn) | d1 D1, d2 D2, . . . , dn Dn} Any set of n-tuples from this Cartesian product is a relation on the n sets. Now let A1, A2, . . ., An be attributes with domains D1, D2, . . . , Dn. Then the set {A1:D1, A2:D2, . . . , An:Dn} is a relation schema. A relation R defined by a relation schema S is a set of mappings from the attribute names to their corresponding domains. Thus, relation R is a set of n-tuples:
(A1:d1, A2:d2, . . . , An:dn) such that d1 D1, d2 D2, . . . , dn Dn Each element in the n-tuple consists of an attribute and a value for that attribute.

Discussed fully in Sections 3.2.2 and 3.2.3.

3.3 Describe the differences between a relation and a relation schema. What is a relational database schema?

A relation schema is a named relation defined by a set of attribute and domain name pairs. A relational database schema is a set of relation schemas, each with a distinct name. Discussed in Section 3.2.3. 3.4 Discuss the properties of a relation.

A relation has the following properties: • has a name that is distinct from all other relation names in the relational schema;
• each cell contains exactly one atomic (single) value; • each attribute has a distinct name; • the values of an attribute are all from the same domain; • each tuple is distinct; there are no duplicate tuples; • the order of

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