Consider a relation R with attributes {A, B, C} and functional dependency set S = {A → B, A → C }. Then relation R can be decomposed into two relations : 

The correct answer is Option 1.

Key Points

• Given a relation R with attributes {A, B, C} and a functional dependency set S = {A → B, A → C}, we can decompose the relation R into two relations.
• Option 1 suggests decomposing R into R1{A, B} and R2{A, C}.
• To verify the correctness of the decomposition:
  • We need to check if both decomposed relations are in BCNF (Boyce-Codd Normal Form) or at least 3NF (Third Normal Form).
  • In R1{A, B}, the functional dependency A → B holds, and A is a candidate key for R1, satisfying BCNF.
  • In R2{A, C}, the functional dependency A → C holds, and A is a candidate key for R2, satisfying BCNF.
• Thus, the decomposition is lossless and dependency preserving, making Option 1 the correct choice.

Additional Information

• Decomposition is a process of breaking down a relation into smaller relations to achieve normalization and eliminate redundancy.
• BCNF is a stricter version of 3NF where every determinant is a candidate key.
• Ensuring that decomposed relations are in BCNF helps maintain data integrity and avoid anomalies during database operations.