The following functional dependencies are given: Which one of the following…
2006
The following functional dependencies are given:
Which one of the following options is false?
- A.
CF+ = {ACDEFG}
- B.
BG+ = {ABCDG}
- C.
AF+ = {ACDEFG}
- D.
AB+ = {ABCDG}
Attempted by 269 students.
Show answer & explanation
Correct answer: C
Solution: compute closures to check each statement.
Closure of {C,F}: Start with C,F. From F -> E add E. From C -> G add G. From G -> A add A. With A and F, AF -> D adds D. Final: CF+ = {A,C,D,E,F,G}. The statement CF+ = {ACDEFG} is correct.
Closure of {B,G}: Start with B,G. From G -> A add A. From A and B, AB -> CD adds C and D. Final: BG+ = {A,B,C,D,G}. The statement BG+ = {ABCDG} is correct.
Closure of {A,F}: Start with A,F. From AF -> D add D. From F -> E add E. With D and E, DE -> F gives nothing new. You cannot derive C or G from these attributes. Final: AF+ = {A,D,E,F}. Therefore the statement AF+ = {ACDEFG} is false.
Closure of {A,B}: Start with A,B. From AB -> CD add C and D. From C -> G add G. Final: AB+ = {A,B,C,D,G}. The statement AB+ = {ABCDG} is correct.
Answer: The false statement is the one claiming AF+ = {ACDEFG}; the correct closure is AF+ = {A,D,E,F}.