3nf functional dependency in wiki's example

Question

I read the wiki about the 3nf https://en.wikipedia.org/wiki/Third_normal_form

it is the example that wiki give

Tournament Winners
Tournament              Year    Winner          Winner Date of Birth
Indiana Invitational    1998    Al Fredrickson  21 July 1975
Cleveland Open          1999    Bob Albertson   28 September 1968
Des Moines Masters      1999    Al Fredrickson  21 July 1975
Indiana Invitational    1999    Chip Masterson  14 March 1977

it say that the non-prime attribute Winner Date of Birth is transitively dependent on the candidate key {Tournament, Year} via the non-prime attribute Winner

I think functional dependency is that

for two row X1 , X2 if X1.col1 = X2.col1 and 
X1.col2 = X2.col2, then col1 -> col2

I cannot understand that Winner Date of Birth->Winner(there may be someone who have same birthday and same name?) and winner can -> candidate key {Tournament, Year} given the winner name Al Fredrickson, it may be Indiana Invitational 1998 or Des Moines Masters 1999)

So, how does it jump to the conclusion?

Answer 1

Informally, a functional dependency means one value on the left side cannot produce multiple values on the right, even when the left side exists in more than one row.¹

So, in Wikipedia example, there is a functional dependency Winner -> Winner Date of Birth, simply because the same winner cannot have different dates of birth even when he/she exists in multiple rows (because he/she won multiple tournaments).

Since...

• {Tournament, Year} -> Winner (since one tournament cannot have multiple winners)
• and Winner -> Winner Date of Birth (as explained above)
• and not Winner -> {Tournament, Year} (since one person can win multiple tournaments)

...then by definition there is a transitive dependency.

I cannot understand that Winner Date of Birth->Winner(there may be someone who have same birthday and same name?)

You flipped the direction. The functional dependency is not "from" the single value, it's "toward" it. Therefore Winner -> Winner Date of Birth, but not Winner Date of Birth -> Winner.

BTW, There cannot be two people with different names in this model. A better (more realistic) model would probably use a surrogate key to identify people, allowing for duplicated names.

---

¹ Which is compliant with the mathematical concept of "function". No matter how many times you "call" a function (i.e. how many rows contain the f.d. left side), it always produces the same "result" (the f.d. right side). If it could produce multiple results, it would not be a function, it would be a "relation".

Answer 2

From what I understand:
For any {Tournament, Year} you have only one winner. Each winner has only one date of birth. Wiki claims that this can lead to vulnerability:
Assume you have entered a new row: {"Stupid tournament", "2013", "Al Fredrickson", "21 July 2012"} - you've entered an incorrect date of birth!
If you keep another table {WinnerID, WinnerBithday}, you'll prevent that.

Answer 3

What if an entry comes for Same Winner with Different Date of Birth? It is possible then How to prevent them?

From the base

Because each row in the table needs to tell us who won a particular Tournament in a particular Year, the composite key {Tournament, Year} is a minimal set of attributes guaranteed to uniquely identify a row. That is, {Tournament, Year} is a candidate key for the table.

If relation R is going to add same Winner Name with different Date of Birth then it will create another Unique record for the table but it is should not be done. We need unique record but this shows same winner with two different Dates of Birth can be exist in a table.

Even if we think of Duplication of Dates of Birth (for winners) we can split that table in another table and can store {winner,winner date of birth} to prevent duplication like wiki has shown.

reference

as there is nothing to stop the same person from being shown with different dates of birth on different records.

That's why it needs to create another table to prevent duplication.