## A functional dependency X Y holds over relation R if, for every allowable instance r of R:

- t1 r, t2 r, (t1) = (t2) implies (t1) = (t2)
- i.e., given two tuples in r, if the X values agree, then the Y values must also agree. (X and Y are sets of attributes.)

## An FD is a statement about all allowable relations.

- Must be identified based on semantics of application.
- Given some allowable instance r1 of R, we can check if it violates some FD f, but we cannot tell if f holds over R!

## K is a candidate key for R means that K R

- However, K R does not require K to be minimal!

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