Question

Consider the table and four functional dependencies below. Which of these dependencies hold on the table and which not?

E 1. D,E- A 1 B,C,D-A A B C D | 2|3|1| 3 2 3 1 2 2 4 1 1 1 5 1 2 2 4 3 1 2 3 1 2 1 3 2 3 2 3. A,D,E-B,C 4. B,D,E-A,C

Answer 1

A functional dependency A->B holds if two rows having same value of attribute A also have same value for attribute B

1, D,E --> A doesnot hold

Reason :-

when D,E has 2,2 values then A holds two different values ie 1 in 4th row and 2 in 6th row. So this functional dependency doesnot hold to this table.

2. B,C,D --> A holds

Reason:-

Eventhough 2nd row and 6th row are repeated B,C,D i.e 3,1,2 their A value is also repeated ie 2 in 2nd row and 6th row.

3. A,D,E --> B,C Doesnot holds

Rason :-

For attribut value of A,D,E ie 2,1,3 in 3rd and 5th row B,C has differnt values ie 4,1 and 4,3.So this functional dependency doesnot hold to this table.

4. B,D,E --> A,C Doesnot holds

Rason :-

For attribut value of B,D,E ie 4,1,3 in 3rd and 5th row B,C has differnt values ie 2,1 and 2,3.So this functional dependency doesnot hold to this table.