Schema Refinement And Functional Dependency

Question 1

Problems due to redundancy

Answer 1

1. Repeated Storage
2. Insertion Anomalies (violation of rule)
3. Updation Anomalies
4. Deletion Anomalies

Question 2

Functional Dependency

Answer 2

(FD)X–>Y
if two tuples agree on value of X they must agree on value of Y

Question 3

Properties of Functional dependency

Answer 3

1. Reflexivity
2. Augmentation
3. Transitivity
4. Union
5. Decomposition

Question 4

Reflexivity

Answer 4

X superset of Y
AB->A, AB->B, AB->AB
Trivial Functional Dependency

Question 5

Augmentation

Answer 5

If X–>Y is a FD then
ZX–>ZY is a FD too

Question 6

Transitivity

Answer 6

If X–>Y is FD and Y–>Z is FD
then X–>Z is FD

Question 7

Union

Answer 7

If X–>Y is FD and X–>Z is FD
then X–>YZ is FD

Question 8

Decomposition

Answer 8

If X–>YZ is FD
then X–>Y and X–>Z is FD

Question 9

Closure Set of Functional Dependencies

Answer 9

Set of all functional dependencies that can be derived using given set F.
Denoted by F+

Question 10

Closure Set of Attributes

Answer 10

Set of all attributes that can be derived using given set X.
Denoted by X+

Question 11

How to find attribute closure

Answer 11

X+ = X if any subset of X is at the LHS of some FD, then add its RHS to X+ and repeat.

Question 12

Closure Set of Functional Dependencies

Answer 12

Set of all functional dependencies that can be derived using given set F.
Denoted by F+

Question 13

Additional set of FD

Answer 13

a functional dependency X–>Y is said to be possible if and only if X+ contains Y.

Question 14

Equivalent FD

Answer 14

F equivalent to G if F+ = G+