Consider the following case study for ER modelling.

We want to create a database for a table tennis tournament. The tournament consists of several matches, each of which is identified by the date, the start time and the end time when the match is held. The database also records the names of the two participating teams (denoted as team 1 and team 2) and the score for each match.

Each player (name and date of birth, which together are unique) belongs to a team which is identified by a team name and is managed by a team coach. The team coach is not a player and is simply identified by his/her name. No two teams are allowed to have the same coach. Each team is led by a captain who himself/herself is also a player. A captain can only lead one team. A team needs to have a number of players.

Teams participate in a number of matches, but not necessarily all of them as teams could give up some of the matches and it is possible that a team is absent from all matches. It is also possible that there are not any teams participating in a match. For each match that a team participates in, the final result (either win or loss) will be recorded.

Matches are divided into either preliminary, semi-final and final matches. There are no other kinds of matches in the tournament and these three types of matches are disjoint. For a preliminary match, the group of the teams involved will be recorded (e.g., a preliminary match for the teams in Group A). For a semi-final or final match, the database records the stage of the match (namely semi-final or final).

Your task: Draw an Entity-Relationship diagram for this database using UML notation. Be sure to include all the entities mentioned above, together with attributes (including primary key attributes), relationships and multiplicity constraints. Note that generalization/specification will be involved in the ER diagram.

Important Notes: Please follow these guidelines carefully: Please ONLY include the following entities in the ER diagram: Team, Player, Match, Coach, Preliminary Match, Semi-final Match and Final Match. The last three entities correspond to the different types of matches. It is possible that there is more than one relationship between two entities in the diagram; Use the UML notation to draw the ER diagrams (i.e., the way of ER modeling taught in the lectures and pracs);

Only use the attributes given in the instruction. Please do not make up any other attributes yourself or use other names for the attributes; Indicate the primary keys for the entities created in the ER diagram. Do not use any artificial primary key (such as matchnumber). All the attributes for natural primary keys are provided in the description.