A · Compressed recap
A relationship links entities; its type is in the schema and its set (instance) is a subset of the product of its entity sets. Degree: unary/recursive (needs roles), binary, ternary. Relationship attributes describe the pair (grade on ENROLLS).
Cardinality ratio (max): 1:1, 1:N, M:N; in Chen notation the number next to E says how many E's a partner can have. Participation (min): total (double line) or partial. (min, max) next to E counts E's own links, so its N sits on the opposite side from Chen's. Attributes of 1:1/1:N relationships can move to the N-side entity; M:N cannot.
Weak entity: no own key; key = owner key + partial key; double rectangle, double diamond, total participation, usually 1:N from owner. EER: subclasses inherit everything; specialisation (top-down) vs generalisation (bottom-up); disjoint/overlapping and total/partial; aggregation lets a relationship join another relationship.
B · Merged rule card
1.2.1 Relationship, relationship set, degree, roles, relationship attributes
- Relationship = association of entities; relationship type (schema), relationship set (instance) ⊆ E₁ × E₂ × …
- Diamond in Chen notation.
- Degree: unary/recursive (1 type), binary (2), ternary (3).
- Recursive relationships need role names.
- Relationship attributes describe the association (grade on ENROLLS).
- Max size of a binary relationship set = |E₁| × |E₂|.
1.2.2 Cardinality ratios; total vs partial participation; (min,max) notation
- Cardinality ratio (max): 1:1, 1:N, N:1, M:N. Chen: the number next to E = how many E's one partner can have.
- Participation (min): total (double line, every entity ≥ 1) or partial (may be 0).
- (min, max) next to E: each entity of E takes part in min..max relationships; min 0 = partial, min ≥ 1 = total. The "N" sits on the opposite side from Chen notation.
- Sizes: 1:1 ≤ min(a, b); 1:N (A one side) ≤ b; M:N ≤ a·b; total N-side participation in 1:N → exactly b.
- Relationship attributes of 1:1 / 1:N may move to an entity (the N side); M:N cannot.
1.2.3 Weak entity sets, identifying relationship, partial key
- Weak entity type: no key of its own; identified via an owner entity + partial key.
- Key(weak) = key(owner) + partial key (discriminator).
- Identifying relationship: double diamond; weak side total participation (double line); usually 1:N owner:weak.
- Notation: double rectangle (weak), double diamond (identifying), dashed underline (partial key).
- Deleting the owner deletes its weak entities.
1.2.4 Extended ER: specialization, generalization, aggregation
- Subclass IS-A superclass; inherits all attributes and relationships; adds local ones.
- Specialisation = top-down; generalisation = bottom-up; same diagram.
- Disjoint (at most one subclass) vs overlapping (several); total (must be in one, double line) vs partial.
- Aggregation: treat a relationship + its entities as an entity so it can join another relationship.
C · Interleaved GATE-style questions
Q1 · MCQ · 1 mark(s) — Ratio
"A course is taught by exactly one faculty member; a faculty member teaches many courses." TEACHES(FACULTY, COURSE) is:
- (A) 1:N from FACULTY to COURSE
- (B) N:1 from FACULTY to COURSE
- (C) 1:1
- (D) M:N
Q2 · MCQ · 2 mark(s) — (min,max)
In (min, max) notation, TEACHES shows FACULTY (0, 3) and COURSE (1, 1). Which is true?
- (A) Each faculty member teaches exactly one course.
- (B) Every faculty member teaches at least one course.
- (C) Each course is taught by exactly one faculty member, and a faculty member teaches at most 3.
- (D) Each course is taught by up to 3 faculty members.
Q3 · NAT · 2 mark(s) — Counting
DEPARTMENT has 8 entities and COURSE has 40. OFFERS is 1:N from DEPARTMENT to COURSE, with total participation of COURSE. How many relationships are in OFFERS?
Numerical answer: ________
Q4 · MCQ · 1 mark(s) — Weak entity
SECTION is a weak entity with owner COURSE (key cid) and partial key sec_no. The key of SECTION is:
- (A) sec_no
- (B) SECTION has no key at all
- (C) cid
- (D) (cid, sec_no)
Q5 · MSQ · 2 mark(s) — Notation
Which "double" symbols are correctly matched?
- (A) double ellipse – derived attribute
- (B) double diamond – identifying relationship
- (C) double line – total participation
- (D) double rectangle – weak entity type
Q6 · MCQ · 1 mark(s) — Degree
SUPERVISES(EMPLOYEE, EMPLOYEE) is:
- (A) ternary
- (B) binary between two entity types
- (C) an identifying relationship
- (D) recursive (unary)
Q7 · MCQ · 2 mark(s) — EER
Every PERSON is an EMPLOYEE, a CUSTOMER, or both. The specialisation is:
- (A) overlapping, partial
- (B) overlapping, total
- (C) disjoint, partial
- (D) disjoint, total
Q8 · NAT · 1 mark(s) — Counting
STUDENT has 7 entities and CLUB has 4. ENROLLS_IN(STUDENT, CLUB) is M:N. What is the maximum number of relationships?
Numerical answer: ________
Q9 · MCQ · 1 mark(s) — Aggregation
Which situation needs aggregation?
- (A) A sponsor funds a particular student–project assignment
- (B) PG students have a thesis title
- (C) Rooms are numbered within buildings
- (D) A student has several phone numbers
D · Answer Vault
Reveal answers when you’re ready
Q1 Answer: (A) · 1 mark(s)
One faculty, many courses.
- (B) is wrong: Reversed.
- (C) is wrong: Faculty teach many.
- (D) is wrong: Each course has one faculty member.
Re-read: Lesson 1.2.2 — Cardinality ratios; total vs partial participation; (min,max) notation
Q2 Answer: (C) · 2 mark(s)
COURSE's (1,1): one teacher each. FACULTY's (0,3): zero to three courses.
- (A) is wrong: Reads the pair from the wrong side.
- (B) is wrong: Min is 0.
- (D) is wrong: Reads the pair from the wrong side.
Re-read: Lesson 1.2.2 — Cardinality ratios; total vs partial participation; (min,max) notation
Q3 Answer: 40 · 2 mark(s)
Each course exactly once: 40.
Re-read: Lesson 1.2.2 — Cardinality ratios; total vs partial participation; (min,max) notation
Q4 Answer: (D) · 1 mark(s)
Owner key + partial key.
- (A) is wrong: Repeats across courses.
- (B) is wrong: It has a key via its owner.
- (C) is wrong: Repeats across sections.
Re-read: Lesson 1.2.3 — Weak entity sets, identifying relationship, partial key
Q5 Answer: (B) (C) (D) · 2 mark(s)
Double ellipse is multivalued; derived is dashed.
- (A) is wrong: Dashed ellipse is derived.
Re-read: Lesson 1.2.3 — Weak entity sets, identifying relationship, partial key
Q6 Answer: (D) · 1 mark(s)
Same entity type twice; needs roles.
- (A) is wrong: No.
- (B) is wrong: Only one entity type.
- (C) is wrong: No weak entity.
Re-read: Lesson 1.2.1 — Relationship, relationship set, degree, roles, relationship attributes
Q7 Answer: (B) · 2 mark(s)
"Or both" → overlapping; "every" → total.
- (A) is wrong: "Every" means total.
- (C) is wrong: Both constraints wrong.
- (D) is wrong: Disjoint forbids both.
Re-read: Lesson 1.2.4 — Extended ER: specialization, generalization, aggregation
Q8 Answer: 28 · 1 mark(s)
7 × 4 = 28.
Re-read: Lesson 1.2.1 — Relationship, relationship set, degree, roles, relationship attributes
Q9 Answer: (A) · 1 mark(s)
A relationship (student works on project) takes part in another relationship (funds).
- (B) is wrong: Specialisation.
- (C) is wrong: Weak entity.
- (D) is wrong: Multivalued attribute.
Re-read: Lesson 1.2.4 — Extended ER: specialization, generalization, aggregation