INTRODUCTION TO FUNCTIONAL DEPENDENCIES

As we discussed in previous section, a relation R from set A to B is a function,

if and only if, For every element in A, there is only one unique image in B.

Extending this concept to tables.

Lets say in a table there are two columns, A and B.

Both A and B contain values or data, thus they are both sets.

A->B, means that there is a function from A to B.

A	B
1	a
2	b
3	a
4	c
5	d
6	d

As we can see in the table each element in A is mapped to a unique element in B.

FORMALLY

A->B,

Means, 

           If, 

               row1(A)=a AND there is another row2 such that row2(A)=a

           Then,

                row1(A)=row2(B)=b 

In simple terms if in a table we have two rows with same value ‘a’ in column A, then as A->B,

‘a’ is associated with a unique value ‘b’ in B. Thus whenever we see ‘a’  we can say that value in column B will be ‘b’



TEST YOURSELF

Which of the functional dependencies are valid for the given tables:


1.

Eid	Ename
1	a
2	b
3	b

a.) Eid->Ename

b.) Ename->Eid

c.) none

2.

A	B
1	1
1	2
2	2

a.) A->B

b.) B->A

c.) None

3.

A	B	C
1	1	4
1	2	4
2	1	3
2	2	3
2	4	3

a.) A->B

b.) B->C

c.) B->A

d.) C->B

e.) A->C

f.) C->A

Answers:

1-a 

2-c

3-e,f

NEXT:

VARIOUS USAGES OF FUNCTIONAL DEPENDENCIES:

1) Identifying additional functional dependencies from given functional dependencies
2) Identifying candidate keys
3) Identifying equivalent functional dependencies
4) Finding minimal functional dependencies

METHOD USED (Not the only method)

• CLOSURE SET of attributes