DBMS

if A → B and C is a list of attributes, then AC → BC

Augmentation

if A → BC, then A → B and A → C

Decomposition

lossless decomposition

If the union of decomposed relations R1 and R2 gives the original relation R ie R1 ∪ R2 = R - the intersection of the subrelations is not null e.g. there is a common element - the intersection of both the subrelations must be a super key of one or both of the subrelations

Transitivity

P → Q and Q → T, therefore P → T

Pseudotransitivity

P → Q and QR → S, therefore PR → S

if A → B and BC → D, then AC → D

Pseudo-transitivity

Union

QR → S and QR → U, therefore QR → SU

Union then Pseudotransitivity

QR → S and QR → U, therefore QR → SU P → Q and QR → SU, therefore PR → SU

if B is a subset of A, then A → B

Reflexivity

if A → B and B → C, then A → C

Transitivity

if A → B and A → C, then A → BC

Union

dependency preserving

a decomposition is dependency preserving if the functional dependencies of the relation schema still hold

lossy decomposition

a decomposition where the join of R1 and R2 does not yield the same relation as in R

candidate key

minimal superkey with no redundant values (no extraneous values)

superkey

set of one or more attributes that uniquely identify a tuple