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# Exercise 5: Normalize Algorithms

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

## Exercise 1

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?

## Exercise 2

Consider the relation schema R = {A, B, C, D, E, F, G, H, I ,J} and the set of functional dependencies F = {AB→C, A→DE, B→F, F→GH, D→IJ}

• Apply the algorithm specified in the lecture to find one candidate key of R
• Apply the algorithm specified in lecture to decompose R into 3NF schemas with Dependency Preserving and Lossless Join

## Exercise 3

Consider the relation schema R = {A, B, C, D, E} and the set of functional dependencies F = {AB→C, CD→E, DE→B}

• Apply the algorithm specified in the lecture to find one candidate key of R
• Apply the algorithm specified in lecture to decompose R into 3NF schemas with Dependency Preserving and Lossless Join

## Exercise 4

(Based on exercise 11.30 of textbook Fundamentals of Database Systems)

Consider the relation REFRIG(M, Y, P, MP, C) and the set of functional dependencies F= {M→MP, MY→P,MP→C}

• Evaluate each of the following set of attributes as a candidate key for REFRIG, giving reasons why it can or cannot be a key: M, MY, MC
• Based on the above key determination, state whether the relation REFRIG is in 3NF and in BCNF, giving proper reasons
• Consider the decomposition of REFRIG into D = {R1(M,Y,P), R2(M,MP,C)}.Is this decomposition lossless? Show why?

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