Data-Structures
October 3, 2023
GATE 2005
October 3, 2023
Data-Structures
October 3, 2023
GATE 2005
October 3, 2023

Functional-Dependency

Question 13

The following functional dependencies are given:

  AB → CD, AF → D, DE → F, C → G, F → E, G → A.  

Which one of the following options is false?

A
{CF}+ = {ACDEFG}
B
{BG}+ = {ABCDG}
C
{AF}+ = {ACDEFG}
D
{AB}+ = {ABCDFG}
Question 13 Explanation: 
AB → CD
AF → D
DE → F
C → G
F → E
G → A
CF+ = {G,E,A,D,C,F} = {A,C,D,E,F,G} (✔️)
BG+ = {B,G,A,C,D} = {A,B,C,D,G} (✔️)
AF+ = {D,E,A,F} = {A,D,E,F} (❌)
AB+ = {A,B,C,D,G} (❌)
Correct Answer: C
Question 13 Explanation: 
AB → CD
AF → D
DE → F
C → G
F → E
G → A
CF+ = {G,E,A,D,C,F} = {A,C,D,E,F,G} (✔️)
BG+ = {B,G,A,C,D} = {A,B,C,D,G} (✔️)
AF+ = {D,E,A,F} = {A,D,E,F} (❌)
AB+ = {A,B,C,D,G} (❌)

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