2

I have a schema

R1(A,B,C,D)

with the following functional dependencies

A->B CD->B A->CD CD->A

I need to figure out which is the highest normal form in which the following table exists. Here A is the primary key.

2NF- Since B, C and D are fully dependent on A, 2NF holds.

3NF-Since B,C and D are not transitively dependent on A. 3NF holds.

Since on the LHS of functional dependencies, there are only super keys, BCNF holds.

Is my solution fully correct? or am i lacking something? I feel this is not 100% correct. Here CD is also a key attribute so do I not need to check my non key attributes with it?

3

You are correct, the relation is in 2NF, 3NF, BCNF.

The reason is that the relation has two keys, A and CD.

So the relation is in BCNF (which is a property stronger than 3NF and 2NF) since each determinant of the minimal conver of R1 is a key. Here is one minimal cover:

A → C
A → D
C D → B
C D → A

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