SQL and Relational Theory, 2nd Edition

PROPERTIES OF RELATIONS

Now let’s get back to our examination of basic relational concepts. In this section, I want to focus on some specific properties of relations themselves. First of all, every relation has a heading and a body: The heading is a set of attributes (where by the term attribute I mean, very specifically, an attribute-name/type-name pair, and no two attributes in the same heading have the same attribute name), and the body is a set of tuples that conform to that heading. In the case of the suppliers relation in Figure 1-3, for example, there are four attributes in the heading and five tuples in the body. Note, therefore, that a relation doesn’t really contain tuples—it contains a body, and that body in turn contains the tuples—but we do usually talk as if relations contained tuples directly, for simplicity.

By the way, although it’s strictly correct to say the heading consists of attribute-name/type-name pairs, it’s usual to omit the type names in pictures like Figure 1-3 and hence to pretend the heading is just a set of attribute names. For example, the STATUS attribute does have a type—INTEGER, let’s say—but I didn’t show it in Figure 1-3. But you should never forget it’s there!

Next, the number of attributes in the heading is the degree (sometimes the arity), and the number of tuples in the body is the cardinality. For example, relation S in Figure 1-3 has degree 4 and cardinality 5; likewise, relation P in that figure has degree 5 and cardinality 6, and relation ...