When is a functional dependency F said to be minimal ?

Every dependency in F has a single attribute for its right hand side.

We cannot replace any dependency X A in F with a dependency Y A where Y is a proper subset of X and still have a set of dependency that is equivalent to F.

We cannot remove any dependency from F and still have set of dependency that is equivalent to F.

What is Multivalued dependency ?

Multivalued dependency denoted by X Y specified on relation schema R, where X and Y are both subsets of R, specifies the following constraint on any relation r of R: if two tuples t1 and t2 exist in r such that t1[X] = t2[X] then t3 and t4 should also exist in r with the following properties

t3[x] = t4[X] = t1[X] = t2[X]

t3[Y] = t1[Y] and t4[Y] = t2[Y]

t3[Z] = t2[Z] and t4[Z] = t1[Z]
where [Z = (R-(X U Y)) ]

What is Lossless join property ?

It guarantees that the spurious tuple generation does not occur with respect to relation schemas after decomposition.

What is 1 NF (Normal Form) ?

The domain of attribute must include only atomic (simple, indivisible) values.

What is Fully Functional dependency ?

It is based on concept of full functional dependency. A functional dependency X Y is full functional dependency if removal of any attribute A from X means that the dependency does not hold any more.

What is 2NF ?

A relation schema R is in 2NF if it is in 1NF and every non-prime attribute A in R is fully functionally dependent on primary key.

What is 3NF ?

A relation schema R is in 3NF if it is in 2NF and for every FD X A either of the following is true

X is a Super-key of R.

A is a prime attribute of R.
In other words, if every non prime attribute is non-transitively dependent on primary key.

What is BCNF (Boyce-Codd Normal Form) ?

A relation schema R is in BCNF if it is in 3NF and satisfies an additional constraint that for every FD X A, X must be a candidate key.

What is 4NF ?

A relation schema R is said to be in 4NF if for every Multivalued dependency X Y that holds over R, one of following is true

X is subset or equal to (or) XY = R.

X is a super key.

What is 5NF ?

A Relation schema R is said to be 5NF if for every join dependency {R1, R2, ...,
Rn} that holds R, one the following is true

Ri = R for some i.

The join dependency is implied by the set of FD, over R in which the left side is key of R.