Finding primary key given relation and functional dependencies

Question

Given the relation:

Competitor(PID, EventName, Pname, TeamName, TeamCoach, EventDate, TeamRating)

And the functional dependencies:

PID -> Pname, TeamName, TeamCoach 
TeamName -> TeamCoach 
EventName -> EventDate 
TeamName, EventName -> TeamRating 

Based on my knowledge I believe the primary key is {PID, EventName, TeamName}

The answer provided says that the primary key is {PID, EventName}

Either I am wrong (which is likely) or the answer provided is wrong.

If you could tell me which is right and the method of how you found it, that would be great.

Answer 1

Your answer is superkey key and it can be qualified as primary key. However, it is not the best answer. The best answer is {PID, EventName}. Your answer is not cadiate key.

You can find candidate key by finding closure of it. If it equals {PID, EventName, Pname, TeamName, TeamCoach, EventDate, TeamRating}, it is candidate key. You can find finding closure algorithm in this site: http://www.cs.sfu.ca/CourseCentral/354/jpei/slides/ClosureDecomposition.pdf

The closures of {PID, EventName} :

C={PID, EventName}

Function: PID -> Pname, TeamName, TeamCoach 
C= {PID, EventName, Pname, TeamName, TeamCoach }

Function: EventName -> EventDate
C={PID, EventName, Pname, TeamName, TeamCoach ,EventDate}

Function: TeamName, EventName -> TeamRating 
C={PID, EventName, Pname, TeamName, TeamCoach ,EventDate,TeamRating}