Final answer:
The relation R(A,B,C,D) with functional dependencies {B→C, D→A} is in Boyce-Codd Normal Form (BCNF), which is determined after evaluating that it satisfies the conditions of the first, second, and third normal forms without any violations.
Step-by-step explanation:
The student has asked about determining the highest normal form for a relation R(A,B,C,D) with the given functional dependencies FDs = {B→C, D→A}. To answer this, we need to evaluate the normal forms systematically.
- First Normal Form (1NF): A relation is in 1NF if it has only atomic (indivisible) values. Since we are not provided with any information that suggests non-atomic attributes, we can assume R is in 1NF.
- Second Normal Form (2NF): A relation is in 2NF if it is in 1NF and all non-prime attributes (attributes that are not part of any candidate key) are fully functionally dependent on any candidate key. Since the functional dependencies provided do not indicate any partial dependencies (dependencies on a part of a candidate key), R is in 2NF.
- Third Normal Form (3NF): A relation is in 3NF if it is in 2NF and all attributes are either non-transitively dependent on every key or a member of a candidate key. Given the functional dependencies, there is no evidence of transitive dependencies since B and D seem to be candidate keys, and A and C are dependent on D and B respectively. Therefore, R is in 3NF.
- Boyce-Codd Normal Form (BCNF): A relation is in BCNF if it is in 3NF, and for every one of its non-trivial functional dependencies, X → Y, X is a superkey. In the given relation, both B and D could be candidate keys, and so B → C and D → A do not violate BCNF. We can conclude that the relation R is in BCNF which is generally considered as the highest normal form in practical database design.
Hence, considering the given information, the relation R(A,B,C,D) with its specified functional dependencies is in Boyce-Codd Normal Form.