A · Compressed recap
A relation is a set of tuples over named attributes with domains; degree = number of attributes (fixed by the schema), cardinality = number of tuples (changes with the state). A relation has no duplicate tuples, no tuple order and atomic values (1NF). The relation schema R(A₁..Aₙ) differs from the relation state r(R) ⊆ dom(A₁) × … × dom(Aₙ); max cardinality = product of domain sizes.
NULL marks a missing value (unknown or not applicable); it is not 0 or ''. Arithmetic with NULL gives NULL; any comparison with NULL, even NULL = NULL, gives UNKNOWN; a query keeps a row only when its condition is TRUE; "is null" tests for NULL.
B · Merged rule card
2.1.1 Relation, tuple, attribute, domain, degree, cardinality, schema; properties of relations
- Relation = table = set of tuples; attribute = named column; domain = allowed values.
- Degree (arity) = number of attributes (fixed); cardinality = number of tuples (changes).
- Relation schema R(A₁..Aₙ) vs relation state r(R) ⊆ dom(A₁) × … × dom(Aₙ).
- Properties: no duplicate tuples, unordered tuples, named (unordered) attributes, atomic values (1NF).
- Max cardinality = product of domain sizes; t[A] = value of A in t.
2.1.2 NULL: meaning and basic behaviour
- NULL = missing value (unknown, not applicable, or unknown whether it exists); not 0, not ''.
- Arithmetic with NULL → NULL. Comparison with NULL (even NULL = NULL) → UNKNOWN.
- Queries keep rows whose condition is TRUE; FALSE and UNKNOWN rows are dropped.
- Test with "is null", which is never UNKNOWN.
- Identifying attributes (primary key) must not be NULL.
C · Interleaved GATE-style questions
Q1 · NAT · 1 mark(s) — Degree
A relation has 6 attributes and 1,000 tuples. What is its degree?
Numerical answer: ________
Q2 · NAT · 2 mark(s) — Cardinality
R(A, B) with |dom(A)| = 5, |dom(B)| = 4 currently holds 7 tuples. How many more tuples can still be inserted at most?
Numerical answer: ________
Q3 · MCQ · 1 mark(s) — Properties
Which display is not a valid relation state?
- (A) Rows in random order
- (B) A NULL in a non-key column
- (C) A row repeated twice
- (D) Rows in descending order of roll
Q4 · MCQ · 1 mark(s) — NULL
If a is NULL and b = 3, then a < b is:
- (A) NULL
- (B) UNKNOWN
- (C) TRUE
- (D) FALSE
Q5 · NAT · 2 mark(s) — NULL
Column marks: 35, NULL, 50, NULL, 80, 20. How many rows satisfy marks < 40 OR marks >= 40?
Numerical answer: ________
Q6 · MSQ · 2 mark(s) — Schema vs state
Which are fixed by the relation schema (not the state)?
- (A) Attribute names
- (B) Cardinality
- (C) Domains of the attributes
- (D) Degree
Q7 · MCQ · 1 mark(s) — NULL
Which condition is TRUE for a row whose x is NULL?
- (A) x is null
- (B) x <> 0
- (C) x = x
- (D) x = NULL
Q8 · MCQ · 2 mark(s) — Atomic values
An ER entity STUDENT has a multivalued attribute phone. In the relation STUDENT(roll, name, phone):
- (A) phone must be NULL
- (B) phone must hold a single value; multiple numbers need another design
- (C) phone becomes the key
- (D) phone can hold the set of all phone numbers
D · Answer Vault
Reveal answers when you’re ready
Q1 Answer: 6 · 1 mark(s)
Attributes count.
Re-read: Lesson 2.1.1 — Relation, tuple, attribute, domain, degree, cardinality, schema; properties of relations
Q2 Answer: 13 · 2 mark(s)
Max 5 × 4 = 20; 20 − 7 = 13.
Re-read: Lesson 2.1.1 — Relation, tuple, attribute, domain, degree, cardinality, schema; properties of relations
Q3 Answer: (C) · 1 mark(s)
Duplicates are not allowed.
- (A) is wrong: Allowed.
- (B) is wrong: Allowed.
- (D) is wrong: Display order is irrelevant.
Re-read: Lesson 2.1.1 — Relation, tuple, attribute, domain, degree, cardinality, schema; properties of relations
Q4 Answer: (B) · 1 mark(s)
Comparison with NULL.
- (A) is wrong: The result is a truth value.
- (C) is wrong: Cannot be decided.
- (D) is wrong: Cannot be decided.
Re-read: Lesson 2.1.2 — NULL: meaning and basic behaviour
Q5 Answer: 4 · 2 mark(s)
Only the four non-NULL rows.
Re-read: Lesson 2.1.2 — NULL: meaning and basic behaviour
Q6 Answer: (A) (C) (D) · 2 mark(s)
Cardinality depends on the current tuples.
- (B) is wrong: Changes with the state.
Re-read: Lesson 2.1.1 — Relation, tuple, attribute, domain, degree, cardinality, schema; properties of relations
Q7 Answer: (A) · 1 mark(s)
Only the null test is TRUE.
- (B) is wrong: UNKNOWN.
- (C) is wrong: UNKNOWN.
- (D) is wrong: UNKNOWN.
Re-read: Lesson 2.1.2 — NULL: meaning and basic behaviour
Q8 Answer: (B) · 2 mark(s)
Atomic values only; Lesson 2.4.1 gives the design.
- (A) is wrong: No.
- (C) is wrong: No.
- (D) is wrong: Not atomic.
Re-read: Lesson 2.1.1 — Relation, tuple, attribute, domain, degree, cardinality, schema; properties of relations