Relationship set

A relationship is an association among several entities. A relationship instance in an E-R schema represents an association between the named entities in the real-world enterprise that is being modeled.

A relationship set is a set of relationships of the same type. Formally, it is a mathematical relation on $n\ge 2$ entity sets that are not necessarily distinct.

If $E_1,\cdots ,E_n$ are entity sets, then a relationship set $R$ is a subset of

$$\{(e_1,\cdots ,e_n):e_i\in E_i,i=1,\cdots ,n\}$$

where $(e_1,\cdots ,e_n)$ is a relationship.

The entity sets $E_1,\cdots ,E_n$ are said to participate in the relationship set $R$.

The function that an entity plays in a relationship is called that entity’s role. Each occurrence of an entity set plays a role in the relationship. However, since entity sets participating in a relationship set are generally distinct, roles are implicit and are not usually specified.

An relationship may also have attributes called descriptive attirbutes that are associated with a relationship set.

Nonbinary relationship sets

The number of entity sets that participate in a relationship set is the degree of the relationship set.

• A binary set relationship set is of degree 2.
• A ternary set relationship set is of degree 3.

A relationship set with degree greater than 2 are uncommon in practice.