1. Consider a relation schema R1(A, B, C, D) that satisfies the set of functional dependencies F1 ={A→B, B→C, C→A}. a) Calculate A + and (AC)+ b) Can AB→ C? Justify your answer. c) Find all the candidate keys of R1 using F1 and show your steps to find them.
1. Consider a relation schema R1(A, B, C, D) that satisfies the set of functional dependencies F1 ={A→B, B→C, C→A}.
a) Calculate A + and (AC)+
b) Can AB→ C? Justify your answer.
c) Find all the candidate keys of R1 using F1 and show your steps to find them.
2. Consider a relation schema R2(A, B, C, D) that satisfies the set of functional dependencies F2 = {A→B, C→D, D→AC}.
a) Is (AD) is candidate key of R2? Justify your answer.
b) Is R2 in BCNF? Explain the reason to your answer.
c) If R2 is not in BCNF, give a lossless-join BCNF decomposition of R2. Is this decomposition dependency preserving?
3. Consider a relation schema R3(A, B, C, D, E) that satisfies the set of functional dependencies F3 = {A → BC, AC → BD}.
a) Calculate (AC)+ and (AE)+
b) Is AB → C in F3 +? Justify your answer.
c) Find the canonical cover Fc of F3.
d) Is R3 in 3NF? Explain the reason to your answer. If R3 is not in 3NF, give a lossless-join, dependency preserving 3NF decomposition of R3.
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