When specifying cardinalities, so far only the upper limit for the admitted number of relationship occurrences was indicated. For example, the cardinalities in the following figure indicate that a project can be assigned a maximum number (m) of employees and one employee can participate in a maximum number (n) of projects.

Besides the upper limit, the lower limit specifying the minimum number of relationship occurrences may also be of interest. For this purpose, the cardinalities can be expressed as a letter pair (a,b), for example (see Scheer, Business Process Engineering). The letter pair (a1, b1) in the following figure indicates that every project can participate in at least a1 and at most b1 relationship occurrences of the works in type, which means that every project can be assigned at least a1 and at most b1 employees. The other letter pair (a2, b2) indicates that one employee can participate in at least a2 and in at most b2 projects.

Thus, every relationship is defined by two degrees of complexity (minimum, maximum). The lower limit often has the values 0 and 1, whereas the value range for the upper limit is defined as 1 <= max <= * (where * is 'any number').

A lower limit of min = 0 means that an entity may participate in a relationship, but does not necessarily have to. A lower limit of min = 1 indicates that an entity must participate in at least one relationship.

In the following figure, the lower limits indicate that an employee may participate in a relationship, but does not necessarily have to (min = 0), while a project has to participate in at least one relationship (min = 1). What is expressed here is that there can be employees who are not assigned to a project. In turn, however, every project must be assigned at least one employee.

If minimum values are equal to 0 or 1 and maximum values are equal to 1 or *, the following four cases of a (min,max) notation can be distinguished: (1,1), (1,m), (0,1), and (0,m). Alternatively, the following abbreviated notation can be used (see Schlageter/Stucky, Database systems, 1983, p. 51):

The following figure shows the previous graphical example using the abbreviated notation.