Functional Dependency

A functional dependency between attributes $x$ and $y$ of relation $R$:

• $x\to y$ if whenever two tuples have the same value for $x$, they must have the same value for $y$
• for any two tuples $t_1$ and $t_2$ in any relation instance $r(R):$ if $t_1[x]=t_2[x]$ then we also know that $t_1[y]=t_2[y]$.
• $x\to y$ specifies a constraint on all relational instances $r(R)$.

Examples:

• Social security number determines employee name; $\text{SSN}\to \text{ENAME}$.
• Project number determines project name + location: $\text{PNO}\to \{\text{PNAME},\text{PLOC}\}$.
• Employee SSN and project number determine the hours per week that the employee works on the project: $\{\text{SSN},\text{PNO}\}\to \text{HOURS}$.