1. The following relation schema R, functional dependency set F and decomposition set ρ are given.
R(S,A,I,P), F={S→A,SI→P}, ρ={R1(SA), R2(SIP)},
Please check if ρ keeps Lossless-join property
Sol)
R1(SA) ∩ R2(SIP) → R1(SA) - R2(SIP) (o)
[R1(SA) ∩ R2(SIP)= S
R1(SA) - R2(SIP) = A,
as F(S→ A,SI→P) ]
S→A
Thus
R1(SA) ∩ R2(SIP) →R1
That is Lossless-join
2. Given the following relation schema R, where U={A,B,C,D, E, G},
F={AB→C, C→A, BC→D, ACD→B, D→EG, BE→C, CG→BD, CE→AG}, Please calculate the Canonical Cover of F.
3. Please tell the level of the highest normal form, then decompose it to BCNF if it is not in BCNF.
(1) R={SNO,SNAME,PNO,QTY}
F={SNO→SNAME,SNAME→SNO,(SNO,PNO)→QTY, (SNAME,PNO)→QTY}
(2) SP={ SNO,SNAME,CITY,STATUS },
F={ SNO→SNAME,SNO→CITY, CITY→STATUS }
4. R(A,B,C,D),F={A→B,C→D}, R∈2NF?
ρ={R1(AB),R2(CD)} , is ρ with Dependency Preservation and Lossless-join properties?
5. Given R(A,B,C,D),F={D→B,C→A,A→C},please give the candidate keys, and determine whether R is in 2NF,if not, decompose R into 2NF.
CK: (A,D),(C,D)
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