How to convert these functional dependencies into 3NF?

Question

How can i design a scheme in 3NF with FD's of the form

a -> t;  b -> v;  b -> w;  {a, b} -> {z, k};  w ->y;  w -> m;  a ->s;
b ->j; w -> p;

Answer 1

• FD1: a -> t;
• FD2: b -> v;
• FD3: b -> w;
• FD4: a, b -> z, k;
• FD5: w -> y;
• FD6: w -> m;
• FD7: a -> s;
• FD8: b -> j;
• FD9: w -> p;

Relation R(A,B,J,K,M,P,S,T,V,W,Y,Z); (A,B) is the primary key as it determines all other attributes by the rules of inference.

At least 2NF, no partial dependentcies on the on key attributes.

FDs with partial dependency on primary key are FD1, FD2, FD3, FD7 and FD8. After relation decomposition we have following set of relation which are at least in NF2:

• R1(A,T,S) -- FD1 and FD7
• R2(B,J,M,P,V,W,Y) -- FD2, FD3, FD5, FD6, FD8 and FD9
• R3(A,B,K,Z) -- FD4

At least 3NF, no transitive dependencies on key attributes.

FD5, FD6 and FD9 are transitive dependencies so move them to a separate relation.

• R1(A,T,S) -- FD1 and FD7
• R21(B,J,V,W) -- FD2, FD3 and FD8
• R22(W,M,P,Y) -- FD5, FD6 and FD9
• R3(A,B,K,Z) -- FD4