The questions can come in any order, so make sure you are selecting right option for all questions.
1. Consider the below relation| roll_no | name | dept_name | dept_buildding |
|---|---|---|---|
| 42 | abc | CO | A4 |
| 43 | pqr | IT | A3 |
| 44 | xyz | CO | A4 |
| 45 | xyz | IT | A2 |
| 46 | mno | EC | B2 |
| 4 | jkl | ME | B2 |
Question 1
Which of the following represents a valid functional dependency in the given relation?
(a) roll_no -> name
Question 2
Identify the invalid functional dependency among the options below:
(c) name -> roll_no
Question 3
In the given relation, which functional dependency is valid?
(a) roll_no -> { name, dept_name, dept_building }
Question 4
Which of the following represents a valid functional dependency based on the given relation?
(a) dept_name -> dept_building
Question 5
Identify the invalid functional dependency among the options below:
(c) dept_building -> dept_name
2. Consider relation R(A,B,C,D,E) with functional dependencies:
D -> C, CE -> A, D -> A, AE -> D
Which of the following is a key?
(c) BCE
3. When an FD is reflexive, Y is a subset of X and X refers to the set of attributes, then:
(b) X -> Y holds
4. Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.
F={CH->G, A->BC, B->CFH, E->A, F->EG} is a set of functional dependencies (FDs) so that F + is exactly the set of FDs that hold for R.
How many candidate keys does the relation R have?
(b) 4
5. Consider a relation scheme R = (A, B, C, D, E, H) on which the following functional dependencies hold:
{A —> B, BC ---> D, E, —> C, D —> A}
What are the candidate keys of R?
(d) AEH, BEH, DEH
6. Let relation R(A,B,C,D,E,F,G,H) satisfy the following functional dependencies:
A -> B, CH -> A, B -> E, BD -> C, EG -> H, DE -> F
Which of the following FDs is also guaranteed to be satisfied by R?
(c) CEG -> AB
7. A functional dependency set F = {A -> B, BC -> E, ED -> A, EF -> G, E -> F}.
Find out the closure of (AC).
(d) {A,B,C,E,F,G}
8.
| A | B | C | D |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 1 | 2 | 4 | 4 |
| 2 | 3 | 4 | 6 |
| 3 | 4 | 5 | 7 |
i. B -> D
ii. A -> C
iii. ABC -> D
iv. ABD -> C
Which of the following FD is not valid?
(d) (ii) and (iv) only
9. The following functional dependencies are given:
AB -> CD, AF —> D, DE --> F, C —> G, F —› E, G --> A
Which one of the following options is false?
(c) {AE }+ = {ACDEFG}
10. Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.
F={CH->G, A->BC, B->CFH, E->A, F->EG} is a set of functional dependencies (FDs) so that F + is exactly the set of FDs that hold for R.
How many candidate keys does the relation R have?
(b) 4
Answer the following questions
Question 1
The closure, A+
(a) {A,B,C,E}
Question 2
The closure, (AE)+
(a) {A,B,C,E}
Question 3
The closure, (ADE)+
(c) {A,B,C,D,E,I}
12. Consider a relation with seven attributes ABCDEGH. The following dependencies are given:
AB -> C, AC -> B, AD -> E, B -> D, BC -> A, E -> G
What is the key?
(b) ACH
13. The relation R(A,B,C,D,E,F) with functional dependency set F = {AB -> CD, C -> CA, B -> E, D -> B, E -> F}
The number of candidate keys of a relation R is ______.
(b) 4
14. Let R(P,Q,R,S,T,U) be a relation schema and F = {PQ -> RS, ST -> U, R -> T, U -> S, PT -> R, T -> P} be the set of functional dependencies defined over R.
Which of the following is true?
(c) {QT}+ = {PQRSTU}
Question 1
A determines B if B is a ___ of A in the reflexive rule.
(c) Subset
Question 2
If B is determined by A, then ___ is determined by BC regardless of C in the augmentation rule.
(d) AC
Question 3
In the case of Transitive Rule, A determines B, and B determines C. Therefore, A must also determine ___.
(c) C
Question 4
Union rule states that if A decides B and A decides C, then A must also decide ___.
(b) B and C
Question 5
If A determines B and X determines Y, then AX determines BY based on _______ rule.
(a) Composition
Question 6
If A determines BC, then A determines B and A determines C holds. This is based on ________ rule.
(b) Decomposition
Question 7
If A determines B, and BC determines D, then AC determines D according to the ___ rule.
(d) Pseudo Transitive Rule
16. Consider relation R(A,B,C,D,E) with functional dependencies:
AB -> C, C -> D, BD -> E
Which of the following sets of attributes does not functionally determine E?
(b) ACD
Answer the following questions
Question 1
Which of the following represents the closure of the attribute set {B}?
(b) {B,C}
Question 2
Which of the following represents the closure of the attribute set {A}?
(a) {A,B,C,D}
Question 3
Which of the following represents the closure of the attribute set {C}?
(e) {C}
Question 4
Which of the following represents the closure of the attribute set {D}?
(e) {D}
Question 5
What are the candidate keys of R?
(a) A