refer to wikipedia---

1NF(first normal form):

1. There's no top-to-bottom ordering to the rows.

2.?There's no left-to-right ordering to the columns.

3.? There are no duplicate rows.

4.? Every row-and-column intersection contains exactly one value from the applicable domain (and nothing else).

5.? All columns are regular [i.e. rows have no hidden components such as row IDs, object IDs, or hidden timestamps].

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2NF(second normal form):

if and only if it is in 1NF and every non-prime attribute of the table is dependent on the whole of a candidate key.

A non-prime attribute of a table is an attribute that is not a part of any candidate key of the table.

Not all 2NF tables are free from update anomalies.

A table for which there are no partial functional dependencies on the primary key is typically, but not always, in 2NF.

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3NF(third normal form):

The relation?R (table) is in 2NF

Every non-prime attribute of R is non-transitively dependent (i.e. directly dependent) on every? s uperkey?of R.

A? transitive dependency ?is a? functional dependency ?in which? X ?→? Z ?( X ?determines? Z ) indirectly, by virtue of? X ?→? Y ?and? Y ?→? Z ?(where it is not the case that? Y ?→? X ).

Requiring existence of "the key" ensures that the table is in? 1NF ; requiring that non-key attributes be dependent on "the whole key" ensures? 2NF ; further requiring that non-key attributes be dependent on "nothing but the key" ensures 3NF.

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BCNF(3.5 normal form):

If a? relational schema ?is in BCNF then all redundancy based on functional dependency has been removed, although other types of redundancy may still exist. A relational schema? R ?is in Boyce–Codd normal form? if and only if ?for every one of its? dependencies ? X → Y , at least one of the following conditions hold: ^[4]

• X → Y ?is a trivial functional dependency (Y ? X)
• X ?is a? superkey ?for schema? R

A 3NF table which does not have multiple overlapping candidate keys is guaranteed to be in BCNF.?Depending on what its functional dependencies are, a 3NF table with two or more overlapping candidate keys may or may not be in BCNF

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3NF：只消除非主屬性對主屬性的傳遞依賴；

BCNF：消除所有屬性對主屬性的傳遞依賴。

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4NF(forth normal form)：

A? Table ?is in 4NF? if and only if , for every one of its non-trivial multivalued dependencies? X ? ? Y ,? X ?is a? superkey —that is,? X ?is either a? candidate key ?or a superset thereof.

A? trivial multivalued dependency ? X ? ? Y ?is one where either? Y ?is a subset of? X , or? X ?and? Y ?together form the whole set of attributes of the relation.

Database: Normal form