Relationships: degree (unary/binary/ternary) & cardinality

Relationship type vs instance

A relationship type is a *meaningful association among entity types*, drawn as a line labeled with a present-tense verb phrase (*Registers For*, *Manages*) — defined once as metadata. A relationship instance is a *specific association* between individual entity instances — "Melton completed C++ in June 2017." Same type/instance split as entities. Two entity types can have multiple, distinct relationships between them (EMPLOYEE *Works In* DEPARTMENT and EMPLOYEE *Manages* DEPARTMENT) as long as each captures a different association with its own cardinality.

Degree — how many entity types participate

The degree of a relationship is the *number of entity types that participate*:

- Unary (degree 1, recursive) — one entity type related to itself. EMPLOYEE *Manages* EMPLOYEE; PERSON *Is Married To* PERSON; ITEM *Has Components* ITEM (bill-of-materials). - Binary (degree 2) — two entity types; the most common. Comes in three cardinality flavors: one-to-one, one-to-many, many-to-many. - Ternary (degree 3) — a *simultaneous* association among three entity types. A ternary is NOT three binaries: an attribute like *Unit Cost* on a Vendor–Part–Warehouse supply cannot be pinned to any single pair, so decomposing into binaries loses information. The guideline: convert every ternary (and higher) to an associative entity with three mandatory-one binary relationships (Module 2.5).

Cardinality — the numbers on the line

Each relationship carries two cardinality specs — one read from *each* end — and each spec has a minimum and a maximum.

- Minimum cardinality is 0 or 1. 0 = optional participation (drawn as a small circle ○). 1 = mandatory participation (drawn as a vertical bar |). - Maximum cardinality is one (a vertical bar |) or many (a crow's foot ⋔). A specific fixed max (e.g. *at most 5 projects*) is written as a number near the crow's foot — but fixed maxima are unstable rules, often enforced in application logic rather than the schema.

The inner symbol (nearest the box) is the *maximum*; the outer symbol (further along the line) is the *minimum*. The four combinations and their plain English:

| Notation | Min / Max | Plain English | |---|---|---| | bar … bar | mandatory one (1,1) | must be associated with exactly one | | bar … crow's foot | mandatory many (1,N) | must be associated with one or more | | circle … bar | optional one (0,1) | may be associated with at most one (or none) | | circle … crow's foot | optional many (0,N) | may be associated with zero or more |

Always read both directions. In CUSTOMER—Submits—ORDER: from CUSTOMER, *optional many* (a customer may have zero or more orders); from ORDER, *mandatory one* (every order belongs to exactly one customer).

Worked example — reading the Nurse / Care-Centre diagram

The sample exam draws Nurse and Care Centre with three relationships. Focus on the unary one on Nurse, labeled *Supervises* / *Supervised_by*. At the top end (Supervises) the notation is a bar (max one) — *each nurse is supervised by at most one nurse*. At the bottom end (Supervised_by) the notation is a circle + crow's foot — minimum zero, maximum many.

Translate the circle + crow's foot directly: a nurse may supervise none (the circle = optional, minimum 0), exactly one, or many (the crow's foot = maximum many) other nurses. In one sentence: "each nurse can supervise one, none, or many nurses." That is the true statement. Watch the distractors: *Works_in* relates Nurse to Care Centre with a bar on the Nurse side, so a nurse works in exactly one centre — "more than one care centre" is false. The diagram says nothing about supervision being "discharged," so that option is just noise. The whole skill is mechanical: find each end's circle/bar (minimum) and bar/crow's-foot (maximum), then read it as one of the four canonical phrases.