Functional Dependencies – Decomposition – Normal Forms
Question 1
Consider the relation schema R(A, B, C, D, E, F, G) và and the set of functional dependencies F on R : F = { A → B, BC → F, BD → EG,AD → C, D → F, BEG → FA }. Calculate the following closures with respect to F
- A+
- ACEG+
- BD+
Question 2
(Based on the exercise 10.28 of the textbook: Fundamentals of Database Systems)
Consider the following relation
| A | B | C |
| 10 | b1 | c1 |
| 10 | b2 | c2 |
| 11 | b4 | c1 |
| 12 | b3 | c4 |
| 13 | b1 | c1 |
| 14 | b3 | c4 |
- Which of the following functional dependencies may hold in the above relation: A→B, B→C, C→B.
- Does the above relation have a potential candidate key? Justify your answer.
Question 3
Consider the relation schema R(A,B,C,D,E, G) anh the set of functional dependencies F = {AB→C, C→A, BC→D, ACD→B, D→EG,BE→C, CG→BD, CE→AG}. Does BD → ACG follow from F?
Question 4
(Based on the question 10.19 from textbook)
Consider the followings two sets of functional dependencies F={A→C, AC→D, E→AD, E→H} and G = {A→CD, E→AH}. Check whether they are equivalent
Question 5
Consider the relation schema R(A,B,C,D,E) and the set of functional dependencies F with respect to R. F = { A → B, BC → E, ED → A }
- List all the candidate keys for R.
- Is R in third normal form (3NF)?
- Is R in BCNF?
Question 6
Consider the relation schema R(A, B, C, D, E, F) and the set of functional dependencies G = { AB→C, C → B, ABD → E, F → A}. Consider also the decomposition D of R.
D = { R1 (BC) , R2(AC), R3(ABDE), R4(ABDF) }. Check whether D is lossless join decomposition or not?






