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How the Maximum and Minimum Cardinality Are Expressed In Crow’s Foot E-R Diagrams

Cardinality is a specific term in Entity relationship diagrams that reflects how many entity instances are associated or related to instances of another entity in a particular occurrence. It shows the occurrence of a particular relationship (Imed, 2014). Ordinality is closely related to cardinality in by the fact that it explains the type of relationship established by entities as either optional or mandatory. Cardinality shows a particular maximum number of relationships while ordinality reveals a minimum number of relationships (Imed, 2014).

In Entity-Relationship model (E-R model) there exist two types of cardinality referred to as minimum cardinality and maximum cardinality. Minimum cardinality refers to the minimum total number of entity instances that can take part in relationship instances.  A total number of participants in minimum cardinality is either zero (0) or one (1) (Imed, 2014). If the total number is zero, then participation of that entity in relationship instance is Optional (O) meaning it doesn’t have to be min a relationship in instances of other entities. If cardinality number is one, that means the participation of that particular entity is Mandatory (M), meaning it must take part in a relationship with instances of other entities (Imed, 2014). Minimum cardinality is expressed in binary form, and there exist four types of minimum cardinality.

  1. Optional and optional (O-O)
  2. Optional and mandatory (O-M)
  3. Mandatory and optional (M-O)
  4. Mandatory and Mandatory (M-M)

Maximum cardinality refers to the maximum total number of relationships that can take part in relationship instance (Imed, 2014). There exist three types of maximum cardinality that include

  1. One to one (1:1)
  2. One to many (1: N)
  3. Many to many (N: M)

Minimum and maximum cardinality can be expressed in various notations. The notations that are widely used include Crows Foot notation, Unified Modeling Language (UML), Bachman and Chen notation (Peter, et al., 2015). Minimum cardinality in Crow’s Foot ER diagram notation is expressed using circles and hash marks. Circles are used to indicate minimum cardinality of zero or optional participation while the hash is used to denote minimum cardinality of one or Mandatory participation (Peter, et al., 2015).  Circle or hash symbol is placed on relationship line at a proximal position with a symbol indicating maximum cardinality.

Crows Foot ER diagram represents maximum cardinality using the hash mark to represent maximum cardinality of one. Crows Footmark represents the cardinality of many. Either a hash or crow’s foot symbol is placed next to rectangular symbol representing the specific entity. The symbols are in various combinations that reveal the type of relationships that exists such as 1:1, 1: N, and N: M.

Cardinality is usually expressed in a binary form indicating a relationship that exists between a given entity and another. However, a single entity may have several relationships with other entities in different instances or same instance. Mutual inclusive and mutually exclusive terms and symbols are applied t define maximum and minimum relationships that exist among entities that are related to a single instance (Carlos, & Steven, 2015). Mutually inclusive symbol means that entities (two or more) must be associated with another entity in a given instance. Mutually exclusive symbol denote one of entity must be associated with another entity in a given instance. Refer to index as figure two explains the various relationship symbols discussed.


Carlos C., & Steven M. (2015). Database Systems: Design, Implementation, & Management. USA: Cengage Learning

Imed B. Bottom of Form(2014). Learn Database Systems with Implementation and Examples. USA: Lulu

Peter R., Carlos C., & Keeley C. (2015).Database Systems: Design, Implementation & Management. USA: Cengage Learning

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