October 14, 2023
October 14, 2023
October 14, 2023
###### Database-Management-System
October 14, 2023
 Question 11

Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?

 A A cell in R holds a set instead of an atomic value. B R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key. C R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key. D R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute.
Question 11 Explanation:
R(ABCD)
FDs:
AB → C
BC → A
(BD)+ = BD ✖
(ABD)+ = ABDC ✔
(CBD)+ = CBDA ✔
Candidate keys = {ABD, CBD}
• The relation R is in 3NF, as there are no transitive dependencies.
• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.
• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.
Question 11 Explanation:
R(ABCD)
FDs:
AB → C
BC → A
(BD)+ = BD ✖
(ABD)+ = ABDC ✔
(CBD)+ = CBDA ✔
Candidate keys = {ABD, CBD}
• The relation R is in 3NF, as there are no transitive dependencies.
• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.
• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.