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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