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Explain Functional dependencies
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Functional dependencies:

• Functional dependencies are used to specify formal measures of goodness of relational designs.

• FD are constrain that are derived from the meaning and inter relationship of the data attributes.

• Set of attributes X functionally determines a set of attributes Y if the value of X determines a unique value for Y.

• X $\rightarrow$ Y holds if whenever two tuples have the same value for X, they must have same value for Y.

• If $f_1 [X] = t_2 [X]$ then $t_1 [Y] = t_2 [Y]$

in any relation instance r(R)

• Let a table R have two attributes X and Y, the attribute Y is functionally dependent on attribute X if and only if for each value of X no more than one value of Y is associated.

• Consider the relation as:

emp (Ename, SeN, Bdate, Address, Dnum)

• The list of FD can be

SSN $\rightarrow$ ename

ename $\rightarrow$ Bdate, Address

SSN $\rightarrow$ Dnumber.

• An FD is a property of the attributes in the schema R.

• The constraint must hold on every relation instance r(R)

• If K is the key of R, then K functionally determines all attributes in R.