Question

Please quesiton on database function dependency: Suppose we have relation R (A, B, C, D, E), with some set of FD’s , and we wish to project those FD’s onto relation S (A, B, C). Give the FD’s that hold in S if the FD’s for R are:

c) AB --> D, AC --> E, BC --> D, D --> A, and E --> B.

d) A --> B, B --> C, C --> D, D --> E, and E --> A.

In each case, it is sufficient to give a minimal basis for the full set of FD’s of S.

Answer 1

Functional dependency-is a relationalship between two attribute. one attribute is a primary key and other non-primary key.

x---->y

where x= determinant

y= dependent

(c). AB-->D,AC-->E,BC-->D,D--->A AND E---> B

ANS- AB-->ABD (NOT FD)

AC-->ACEBD { AC-->E,E--->B,BC--->D} ( FD)

D-->AD { D-->A}

NOT FD

E-->BE { E-->B}

functional dependency - AC--> E

(d) A-->B

B-->C

C--->D

D--->E

E--->A

Ans- A-->BACDE { A-->B,B-->C,C--->D,D--->E,E--->A} (FD)

B--->CBDEA { B-->C,C--->D,D--->E,E--->A} (FD)

C--->DCEAB { C-->D,D-->E,E--->A,A--->B } (FD)

D--->EDABC { D-->E,E--->A,A-->B,B--->C} (FD)

E---->AEBCD { E--->A,A-->B,B-->C,C--->D} (FD)

functional dependency- { A,B,C,D,E}