$1.(20$ points$)$ You are asked to design a database system for the NDHU Open Tennis tournament. We need to keep the information of several kinds of entities and relationships. There are human entities such as Players, Judges, Ball Boys and Girls $($BBGs$).$ All human entities have SSN$,$ name, gender and country. Players may or may not be seeded. Players can have different seeding positions on different types of matches. Judges $($also known as empires$)$ have ranking. BBGs have age. There are non$-$human entities such as Courts and Matches. Each court has courtID, name, location and capacity. Each match has a matchID, type, date, time, and court. There are five types of matches: Men$$s Singles, Women$$s Singles, Men$$s Doubles, Women$$s Doubles, and Mix Doubles. All Singles are between two players while Doubles are between two teams of two players each. Each type of matches is divided into seven rounds: Round $1,2,3,4($Round of $16),$ Quarter$-$finals, Semi$-$finals, and Finals. With electronic line$-$calling system, each match needs only one Judge and exactly six BBGs$.$ Tennis scoring system is complex so we will skip it for the first version. However, we still need to keep the record of the result of each match $($the winner$($s$)).$

$1$a$)$ Draw an ER$/$EER diagram to model the above application. Indicate the cardinalities of relationships, as well as the weak entities $($if any$).$ For each entity, designate the primary key$($s$)$; for weak entities, designate the identifying relationship type and owner.

$1$b$)$ Transform the ER$/$EER diagram into a relational database schema. Specify all primary keys, foreign keys and the attribute pointed to by each foreign key.