October 19, 2023
October 19, 2023
October 19, 2023
###### UGC-NET Dec 2019 Part-1
October 19, 2023
 Question 43

R(A,B,C,D) is a relation. Which of the following does not have a lossless join, dependency preserving BCNF decomposition?

 A A → B, B → CD B A → B, B → C, C → D C AB → C, C → AD D A → BCD
Question 43 Explanation:
We have, R (A, B, C, D) and the Functional Dependency set = {AB→C, C→AD}.
We decompose it as R1(A, B, C) and R2(C, D). This preserves all dependencies and the join is lossless too, but the relation R1 is not in BCNF. In R1 we keep ABC together otherwise preserving {AB→C} will fail, but doing so also causes {C→A} to appear in R1. {C→A} violates the condition for R1 to be in BCNF as C is not a super key. Condition that all relations formed after decomposition should be in BCNF is not satisfied here.
Question 43 Explanation:
We have, R (A, B, C, D) and the Functional Dependency set = {AB→C, C→AD}.
We decompose it as R1(A, B, C) and R2(C, D). This preserves all dependencies and the join is lossless too, but the relation R1 is not in BCNF. In R1 we keep ABC together otherwise preserving {AB→C} will fail, but doing so also causes {C→A} to appear in R1. {C→A} violates the condition for R1 to be in BCNF as C is not a super key. Condition that all relations formed after decomposition should be in BCNF is not satisfied here.