3.2 · Cardinality & Participation

Goal: describe relationships precisely.

Cardinality — "how many" on each side

Cardinality	Description
1 : 1 (one-to-one)	Each instance of A relates to at most one of B and vice versa
1 : M (one-to-many)	Each A relates to many B; each B relates to one A
M : N (many-to-many)	Many A to many B

Examples

Relationship	Cardinality
Person — has — Passport	1 : 1
Department — employs — Staff	1 : M
Student — enrols in — Course	M : N

HKEAA symbols (the C&A Guide reproduces these)

1 ────── 1   Relationship   one-to-one
1 ────── M   Relationship   one-to-many
M ────── N   Relationship   many-to-many

Participation — "must / may"

Participation	Notation	Meaning
Total / Mandatory	Double line ══	Every instance must participate
Partial / Optional	Single line ──	An instance may or may not participate

Examples

Relationship	Participation
Loan must reference a Member	Loan side: Mandatory
A Member may or may not have any current Loans	Member side: Optional

Combining cardinality + participation

Example: Member borrows Book

Member ──── < borrows > ════ Book
  (M)   optional ─║║══ mandatory  (N)

Here:

• M:N cardinality (associative entity required).
• Member's participation is optional (some members never borrow).
• Loan's participation is mandatory (every loan record must reference a book).

Resolving M:N — repeat from 3.1

Member ───< Loan >─── Book

Loan becomes its own entity with FKs to both sides.

Cardinality decisions in practice

Ask:

1. Can A exist without B? → optional participation.
2. Can one A relate to more than one B? → many side.
3. Can one B relate to more than one A? → many side.

If both sides are "many" → introduce an associative entity.

Common student mistakes

• Confusing cardinality (numbers) with participation (mandatory / optional).
• Forgetting to mark mandatory side as double line.
• Treating every relationship as M:N.

Exam-style question

Q (5 marks): For each scenario, state the cardinality and participation:

(a) A bank account belongs to exactly one customer; a customer may have multiple accounts. (b) A student takes many courses; each course has many students; both sides are mandatory.

Sample answer:

(a) Cardinality: 1 : M (Customer to Account). Participation: Customer side optional (customer can exist before opening any account); Account side mandatory (every account must have an owner).

(b) Cardinality: M : N (Student to Course). Participation: mandatory on both sides (every student must enrol in at least one course; every course must have at least one student). Implementation requires an associative entity, e.g. Enrolment(student_id, course_id, semester, grade).

Key takeaways

• Cardinality = numbers (1, M, N).
• Participation = whether it's mandatory.
• Pin both down before designing tables.

➡️ Next: 3.3 Normalisation