A reference property (such as chair in the example shown in Figure 11.1 above) can be visualized in a UML class diagram in the form of an association end owned by its domain class. This requires to connect the domain class and the range class of the reference property with an association line and annotate the end of this line at the range class side with a "dot", with the property name and with a multiplicity symbol, as shown in Figure 11.2 below for the case of our example. In this way we get a unidirectional association, the source class of which is the property's domain and the target class of which is the property's range.

The fact that an association end is owned by the class at the other end is visually expressed with the help of a small filled circle (also called a "dot") at the end of the association line. This is illustrated in Figure 11.2 below, where the "dot" at the association end chair indicates that the association end represents a reference property chair in the class Committee having ClubMember as range.

Figure 11.2. A committee has a club member as chair expressed by an association end with a "dot"

Thus, the two diagrams shown in Figure 11.1 and Figure 11.2 express essentially equivalent models. When a reference property is modeled by an association end with a "dot", like chair in Figure 11.1, then the property's multiplicity is attached to the association end. Since in a design model, all association ends need to have a multiplicity, we also have to define a multiplicity for the other end at the side of the Committee class, which represents the inverse of the property. This multiplicity (of the inverse property) is not available in the original property description in the model shown in Figure 11.1, so it has to be added according to the intended semantics of the association. It can be obtained by answering the question "is it mandatory that any ClubMember is the chair of a Committee?" for finding the minimum cardinality and the question "can a ClubMember be the chair of more than one Committee?" for finding the maximum cardinality.

When the value of a property is a set of values from its range, the property is non-functional and its multiplicity is either 0..* or n..* where n > 0. Instead of 0..*, which means "neither mandatory nor functional", we can simply write the asterisk symbol *. The association shown in Figure 11.2 assigns at most one object of type ClubMember as chair to an object of type Committee. Consequently, it's an example of a functional association.

The following table provides an overview about the different cases of functionality of an association:

Notice that the directionality and the functionality type of an association are independent of each other. So, a unidirectional association can be either functional (one-to-one or many-to-one), or non-functional (one-to-many or many-to-many).