Functional Dependancies

Question 1

what is the definition of a functional dependency?

Answer 1

if A and B are attributes in relation R, A -> B if each value of A in R is associated with exactly one value of B
A is the determinant
B is the dependant set

Question 2

what is a trivial functional dependency?

Answer 2

AB -> A is a trivial FD because the dependant set is a subset of the determinant

Question 3

what is a partial functional dependency?

Answer 3

A -> B is a partial functional dependency if you can remove an attribute from A and the dependency still exists

AB -> C C

Question 4

what is a full FD?

Answer 4

the ‘opposite’ of partial. if removing an attribute from the determinant results in the dependancy no longer existing, the FD is full

Question 5

transitive?

Answer 5

A -> B
B -> C
therefore A -> C

Question 6

what is a superkey? candidate key?

Answer 6

attributes K is a superkey of relation R if values for K can be used to uniquely identify a tuple

a candidate key is a minimal set of attributes that can uniquely identify: a minimal superkey

Question 7

what is closure?

Answer 7

given a set F of functional dependancies, there are other FDs that are implied by F
e.g. transistivity A -> C

the set of all FDs logically implied by F is the closure of F, F+

Question 8

what are armstrong’s axioms?

Answer 8

– if B <= A , then A -> B (reflexivity)
– if A -> B, then CA -> CB (augmentation)
– if A -> B, and B-> C, then A -> C (transitivity)
they are sound and complete
they generate only FDs that hold, and ALL the FDs that hold