Database systems 1. Consider a relation with schema R(A,B,C,D) and FD Database s

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Database systems

1. Consider a relation with schema R(A,B,C,D) and FD

Database systems 1. Consider a relation with schema R(A,B,C,D) and FD???s AB->C, C->D, and D->A. a. What are all the keys of R ? b. What are all the superkeys for R that are not keys? c. What is the the closure of {B,D}? 2. For a relation schema R(A,B,C,D,E) with FD???s AB->C, DE->C, B->D, a. indicate all the BCNF violations, and b. indicate all the 3NF violations, and c. decompose the relation as necessary, into collections of relations that are in BCNF.

Explanation / Answer

1.) a) {AB},{CB},{DB} are keys for the given relational schema

b) {ABC},{ABD},{BCD},{ABCD} are superkeys for the given relational schema that are not keys.

c) {B,D} = {B,D,A,C}

2.) a) AB->C, DE->C, B->D are all BCNF violations

b) AB->C, DE->C, B->D are all 3NF violations

c) We decompose R into three relations R1(A,B,C),R2(C,D,E) and R3(B,D)

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