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# Exercise 4: Functional dependencies-Decomposition-Normal Forms

Module by: Nguyen Kim Anh. E-mail the author

## Theory Exercise 4

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?

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