Chapter 7, Problem 21E

Explanation of Solution

Lossless decomposition of schema R into Boyce Code Normal Form(BCNF):

• From Practice Exercises 7.1, $\text{B}\to \text{D}$ is non-trivial and the left hand side is not a super key.
• Consider the algorithm,
  • result: = {R};
  • F={$\text{A}\to \text{ABCDE,B}\to \text{D,CD}\to \text{ABCDE,BC}\to \text{ABCDE,E}\to \text{ABCDE,}$….}
  • A schema “R” is not in BCNF.
  • A non-trivial one is $\text{B}\to \text{D}$ that highly holds on, $\text{B}\cap \text{D}=\varnothing$