An Introduction to Second and Third Normal Form

Practice Designing and Querying Multiple Table Databases

First Normal Form:

  1. each row contains atomic values
  2. each row has a unique identifier - primary key

For example, this table

band members
Coldplay Chris Martin, Jonny Buckland, Guy Berryman
Chainsmokers Andrew Taggart, Alex Pall
Fall Out Boy Patrick Stump, Joe Trohman, Pete Wentz

does not contain atomic values because the members column has multiple values of the same type (Chris Martin and Jonny Buckland are the same type of thing and there are multiple of those in a cell )

This next table is also not atomic because multiple columns represent the same sort of thing (member1, member2, member3).

band member1 member2 member3
Coldplay Chris Martin Jonny Buckland Guy Berryman
Chainsmokers Andrew Taggart Alex Pall  
Fall Out Boy Patrick Stump Joe Trohman Pete Wentz

The following table meets both criteria of First Normal Form (1NF) because all the values are atomic and each row has a unique key. The username is unique and in the table we represent the primary key with PK:

username (PK) firstname lastname password
daiho Jill Miller 123456
mitsugo Ann Mulkern password
awe Adam Waite qwerty
lingual Ann Miller password

Synthetic Primary Key is a key that is not part of the original Data. So the username column in the table above was not a synthetic primary key but the id column in the following table is:

id (PK) city state ST population
1 Santa Fe New Mexico NM 67947
2 Santa Fe Texas TX 12222
3 Springfield Massaschusetts MA 15360
4 Springfield Illinois IL 11706

Alternatively we can make a two column primary key. So, for example, the city and state columns combined may be unique:

city (PK) state (PK) ST population
Santa Fe New Mexico NM 67947
Santa Fe Texas TX 12222
Springfield Massaschusetts MA 15360
Springfield Illinois IL 11706

This is called a Composite key (a key made up of more than one column.)

Functional Dependency

The value of one column depends on another column.

Partial Functional Dependency

Some non-key column is dependent is dependent on some but not all of the columns of the composite key.

Transitive Functional Dependency

A non-key column is related to another non-key column

So in the above table repeated here:

city (PK) state (PK) ST population
Santa Fe New Mexico NM 67947
Santa Fe Texas TX 12222
Springfield Massaschusetts MA 15360
Springfield Illinois IL 11706

We have a functional dependency between the ST column and the state column. If we change the value in the state column we would need to change the value in the ST column. It is a partial functional dependency by definition (some non-key column is dependent is dependent on some but not all of the columns of the composite key).

Second Normal Form

  1. The table needs to be in 1NF
  2. The table cannot have any partial functional dependencies.

Third Normal Form

  1. The table needs to be in 2NF
  2. The table has no transitive functional dependencies

Suppose we have a university class schedule:

crn (PK) course title section credits days
10405 cpsc110 Introduction to computer science 4 3 MWF
10406 cpsc110 Introduction to computer science 3 3 TTh
13091 musp301 Intermediate Piano 1 1 TBD
13092 musp301 Intermediate Piano 2 1 TBD

If a table is in 1NF and has a one column primary key it is in 2NF. This table is in 2NF but not 3NF. The title column is dependent on the course column and this is a transitive functional dependency.

The solution is to divide the table into two tables:


crn (PK) course section days
10405 cpsc110 4 MWF
10406 cpsc110 3 TTh
13091 musp301 1 TBD
13092 musp301 2 TBD


course (PK) title section days
cpsc110 Introduction to computer science 4 MWF
cpsc110 Introduction to computer science 3 TTh
musp301 Intermediate Piano 1 TBD
musp301 Intermediate Piano 2 TBD

In the sections table, the course column is a foreign key.

	 title TEXT,
	 credits, NUMERIC,
	 si CHAR(1));
CREATE TABLE sections 
	 course TEXT REFERENCES courses (course),
	 section NUMERIC,
	 days TEXT);

Suppose we want to find the course (cpsc110) and title (Introduction to Computer Science) that meet on TTh:

SELECT courses.course, courses.title FROM courses 
JOIN sections ON courses.course = sections.course 
WHERE sections.days = 'TTh';


This table is in 1NF but not 2NF.

band member member real name band formed birthplace
Imagine Dragons Dan Reynolds Daniel Reynolds 2008 Las Vegas, NV
Imagine Dragons Wing Sermon Daniel Wayne Sermon 2008 American Fork, UT
Imagine Dragons . Daniel Platzman Daniel Platzman 2008 Atlanta, GA
Imagine Dragons Ben McKee Benjamin Arthur McKee 2008 Forestville, CA
Egyptian Dan Reynolds Daniel Reynolds 2010 Las Vegas, NV
Egyptian Aja Volkman Aja Volkman-Reynolds 2010 Eugene, OR

A quick discussion of different types of relations

  • 1:1. (ex, a course like cpsc110 to a course title Intro to cs ) Can be represented in 1 table.
  • 1: Many. (ex, a publisher to a book) This requires at least 2 tables.
  • Many : Many (ex, bands to band members – bands have multiple band members, and a member can be in multiple bands) This requires a junction table. 3 tables


band-id (PK) name genre yr_formed
1 Imagine Dragons alternative rock 2008
2 Egyptian alternative rock 2010
3 Baby Metal heavy metal 2010
4 Sakura Gakuin J-Pop 2010
5 Earth, Wind & Fire funk 1969
musician_id (PK) member member_real_name birthplace
1 Dan Reynolds Daniel Reynolds Las Vegas, NV
2 Wing Sermon Daniel Wayne Sermon American Fork, UT
3 Daniel Platzman Daniel Platzman Altlanta, FA
4 Ben McKee Benjamin Arthur McKee Forestville, CA
5 Aja Volkman Aja Volkman-Reynolds Eugene, OR

We connect this table with a junction table:

band_id (PK) musician_id (PK)
1 1
1 2
1 3
1 4
2 1
2 6

We can represent this as follows:


\c bands;

  band_id integer PRIMARY KEY,
  name text,
  genre text,
  formed integer

INSERT INTO band (band_id, name, genre, formed) VALUES (1, 'Baby Metal', 'heavy metal', 2010), 
                                         (2, 'Imagine Dragons', 'alternative rock', 2008), 
                                         (3, 'Sakura Gakuin', 'J-pop', 2010), 
                                         (4, 'Egyptian', 'alternative rock', 2010),
                                         (5, 'Earth Wind & Fire', 'funk', 1969);

  musician_id integer PRIMARY KEY,
  stagename text,
  realname text,
  origin text,
  birthdate DATE

INSERT INTO musician (musician_id, stagename, realname, origin, birthdate) VALUES 
    (1, 'Su-Metal', 'Suzuka Nakamoto', 'Hiroshima Prefecture, Japan', '1997-12-20'), 
    (2, 'MoaMetal', 'Moa Kikuchi', '  Kanagawa Prefecture, Japan', '1999-7-4'),
    (3, 'YuiMetal', 'Yui Mizuno', 'Aichi Prefecture, Japan', '1999-06-20'), 
    (4, 'Aiko Yamaide', 'Aiko Yamaide', 'Kagoshima Prefecture, Japan', '2002-12-01'),
    (5, 'Mariri Sugimoto', 'Mariri Sugimoto', 'Hiroshima Prefecture, Japan', '2000-08-04'), 
    (6, 'Hana Taguchi', 'Hana Taguchi', 'Nagano Prefecture, Japan', '1999-7-4'),
    (7, 'Dan Reynolds', 'Daniel Reynolds', 'Las Vegas, Nevada, United States', '1987-07-14'), 
    (8, 'Wing', 'Daniel Wayne Sermon', '  American Fork, Utah, United States', NULL),
    (9, 'Aja Volkman-Reynolds', 'Aja Volkman-Reynolds', 'Eugene, OR', '1987-01-01'),
    (10, 'Daniel Platzman', 'Daniel Platzman', '  Atlanta, Georgia, United States', '1986-09-28'),
    (11, 'Ben McKee', 'Benjamin Arthur McKee', 'Forestville, California, United States', '1985-04-07');

create table bandmember (
  band_id integer REFERENCES band(band_id),
  member_id integer REFERENCES musician(musician_id),
  PRIMARY KEY (band_id, member_id));
INSERT INTO bandmember VALUES (1, 1), (1, 2), (1, 3), 
     (2, 7), (2, 8), (2, 10), (2, 11),
     (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
     (4, 7), (4, 9);

create table instrument (
  id integer PRIMARY KEY,
  name text,
  family text

insert into instrument (id, name, family) VALUES (1, 'vocals', 'voice'), 
   (2, 'screams', 'voice'), (3, 'dance', 'dance'),
   (4, 'koto', 'string'), (5, 'electric guitar', 'string'), (6, 'drums', 'percussion'), (7, 'bass', 'string'), (8, 'keyboards', 'keyboards');

create table plays (
  member_id integer REFERENCES musician(musician_id),
  instrument_id integer REFERENCES instrument(id),
  PRIMARY KEY (member_id, instrument_id));
insert into plays VALUES (1, 1), (1, 3), (2, 2), (2, 3), (3, 2), (3,3), 
   (7, 1), (7, 8), (8, 5), (9, 1), (9,8), (10, 6), (10,1), (11, 7); 
finding all the band members of Imagine Dragons
SELECT musician.stagename FROM musician 
JOIN bandmember ON 
musician.musician_id = bandmember.member_id 
JOIN band ON 
bandmember.band_id = band.band_id 
WHERE = 'Imagine Dragons';

 	Dan Reynolds
 	Daniel Platzman
 	Ben McKee
(4 rows)
What instruments does BenMcKee
SELECT FROM instrument 
JOIN plays ON = plays.instrument_id 
JOIN musician  ON 
musician.musician_id = plays.member_id 
WHERE musician.stagename = 'Ben McKee';

Queries that require multiple copies of a table

Suppose as part of the bands database we have a table specifying who is friends with whom.

CREATE TABLE friends (
person INTEGER REFERENCES musician(musician_id),
friends_with INTEGER REFERENCES musician(musician_id));

 INSERT INTO friends (person, friends_with) VALUES
  (7, 8),
  (7, 9),
  (9, 11);   

For example, the first insert represents that Dan Reynolds is friends with Wing. Let’s consider how we would write a query to find out who is Dan Reynolds friends with. At first we might think to write:

SELECT musician.stagename FROM musician 
JOIN friends ON musician.musician_id = friends.person 
WHERE musician.stagename = 'Dan Reynolds';

You will see that this doesn’t work as all it returns is Dan Reynolds

For this query we actually need two copies of the musicians table– one to find the musician_id of Dan Reynolds. Once we find out his id is 7, look at the friends table and discover he is friends with id 8, we need another table to lookup the stagename for id 8. We implement it as follows:

SELECT m1.stagename FROM musician as m1 
JOIN friends ON m1.musician_id = friends.friends_with 
JOIN musician as m2 ON friends.person = m2.musician_id 
WHERE m2.stagename = 'Dan Reynolds';

  Aja Volkman-Reynolds
 (2 rows)

Suppose we want to know who is in bands with Dan Reynolds. For that the query is

SELECT m1.stagename FROM musician as m1 
  JOIN bandmember AS b1 ON m1.musician_id = b1.member_id 
  JOIN bandmember as b2 ON b1.band_id = b2.band_id 
  JOIN musician AS m2 ON m2.musician_id = b2.member_id 
  WHERE m1.stagename <> 'Dan Reynolds' 
  AND m2.stagename = 'Dan Reynolds';

Question: why do we have m1.stagename <> 'Dan Reynolds' ?

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