Relationship, relationship set, degree, roles, relationship attributes

0 · Recall Warm-up

Answer from memory first. Answers are in the Answer Vault at the bottom.

1. What is a key attribute, and how is it drawn? from Lesson 1.1.2
2. Composite or multivalued: a student's several phone numbers? from Lesson 1.1.2
3. What is the Cartesian product A × B? from Lesson 0.2.2

1 · The Hook

Asha takes the DBMS course and the Networks course and gets an A in DBMS. That fact is not about Asha alone or about DBMS alone: it is about Asha and DBMS together. The grade belongs to the pair. ER models such facts as relationships.

2 · Predict First

Where should Asha's grade "A in DBMS" be stored: as an attribute of STUDENT, as an attribute of COURSE, or somewhere else?

Make a guess in your head. The answer opens Section 3.

3 · Core Concept

Predict First — the answer

Somewhere else: on the relationship between Asha and DBMS. Asha has a different grade in each course, and each course gives different grades to different students, so the grade depends on the pair. It is a relationship attribute of ENROLLS.

Relationship, relationship type, relationship set

• A relationship is an association between entities: (Asha, DBMS) means "Asha enrols in DBMS".
• A relationship type (schema) such as ENROLLS(STUDENT, COURSE) names the kind of association and the entity types that take part.
• A relationship set (instance) is the set of relationships stored now: {(Asha, DBMS), (Asha, Networks), (Chirag, DBMS), …}.

Since every relationship picks one student and one course, a relationship set of type ENROLLS is a subset of STUDENT × COURSE (Lesson 0.2.2). This is why a relationship set never holds the same pair twice.

Chen notation: diamond joined by lines to the participating entity types.

Degree

The degree of a relationship type is the number of entity types taking part.

• Binary (degree 2): ENROLLS(STUDENT, COURSE). The most common.
• Ternary (degree 3): TEACHES(FACULTY, COURSE, SEMESTER): "Prof. Rao teaches DBMS in Monsoon 2026".
• Unary / recursive (degree 1): an entity type related to itself. MENTORS(STUDENT, STUDENT): a senior student mentors a junior.

Roles

Each entity type in a relationship plays a role. In ENROLLS the roles are obvious. In a recursive relationship the same entity type appears twice, so the roles must be named: in MENTORS one student plays mentor and the other plays mentee. Role names are written on the lines.

Relationship attributes

A relationship type can have attributes, drawn as ellipses on the diamond. grade on ENROLLS; since_date on WORKS_IN. A relationship attribute describes the association, not either entity alone.

Later (Lesson 1.2.2) you will see that for 1:1 or 1:N relationships such an attribute could be moved to one of the entities; for M:N it must stay on the relationship.

4 · Visual

Binary ENROLLS with a relationship attribute (grade); recursive MENTORS with role names.

5 · Worked Examples

Example 1 Easy

Name the degree: (a) WORKS_IN(FACULTY, DEPARTMENT); (b) SUPPLIES(SUPPLIER, PART, PROJECT); (c) REPORTS_TO(EMPLOYEE, EMPLOYEE).

Solution

(a) binary; (b) ternary; (c) unary (recursive), needing roles such as boss and subordinate.

Example 2 Medium

STUDENT has 4 entities and COURSE has 3. What is the largest possible number of relationships in the ENROLLS relationship set?

Solution

The set is a subset of STUDENT × COURSE, which has 4 × 3 = 12 pairs. So at most 12.

Example 3 GATE

Where should each attribute go: (a) the date a faculty member joined a department, where each faculty member is in exactly one department; (b) the marks a student gets in a course?

Solution

(b) marks must be on ENROLLS (it depends on the pair, and a student takes many courses while a course has many students). (a) may be placed on WORKS_IN or, because each faculty member has exactly one department, moved to FACULTY. Lesson 1.2.2 explains why the "one" side allows the move.

8 · Connect the Dots

Lesson 1.1.2 gave keys to tell entities apart; this lesson linked entities with relationships. Next: how many entities can be linked on each side (1:1, 1:N, M:N) and whether every entity must be linked: the most-tested ER idea in GATE.

9 · Self-Test

GATE format. Try every question before opening the vault.

Q1 · MCQ · 1 mark(s) — Degree

A relationship that links three entity types is:

1. (A) weak
2. (B) binary
3. (C) ternary
4. (D) recursive

Q2 · MCQ · 1 mark(s) — Notation

A relationship type is drawn as a:

1. (A) double rectangle
2. (B) rectangle
3. (C) diamond
4. (D) ellipse

Q3 · NAT · 1 mark(s) — Counting

FACULTY has 6 entities and COURSE has 5. What is the maximum number of relationships in TEACHES(FACULTY, COURSE)?

Numerical answer: ________

Q4 · MCQ · 2 mark(s) — Relationship attribute

A student's grade in a course should be modelled as:

1. (A) an attribute of the ENROLLS relationship
2. (B) a separate entity type GRADE with no relationships
3. (C) an attribute of COURSE
4. (D) an attribute of STUDENT

Q5 · MCQ · 1 mark(s) — Roles

In MENTORS(STUDENT, STUDENT), role names are needed because:

1. (A) it is ternary
2. (B) the same entity type appears twice
3. (C) STUDENT has no key
4. (D) the relationship has an attribute

11 · Concept Ledger

Unlocked in this lesson. From here on, these terms may be used.

relationshiprelationship typerelationship setdegreebinaryternaryunary (recursive) relationshiprolerelationship attributeChen diamond