Consider a database system for a baseball organization such as the major leagues. The data requirements are summarized as follows: 

• The personnel involved in the league include players, coaches, managers, and umpires. Each is identified by a unique personnel id. They are also described by their first and last names along with the date and place of birth.
• Players are further described by other attributes such as their batting orientation (left, right, or switch) and have a lifetime batting average (BA). 

• Within the players group is a subset of players called pitchers. Pitchers have a life time ERA (earned run average) associated with them. 

• Teams are uniquely identified by their names. Teams are also described by the city in which they are located and the division and league in which they play (such as Central division of the American league). 

• Teams have one manager, a number of coaches, and a number of players. 

• Games are played between two teams with one designated as the home team and the other the visiting team on a particular date. The score (runs, hits, and errors) are recorded for each team. The team with more number of runs is declared the winner of the game. 

• With each finished game, a winning pitcher and a losing pitcher are recorded. In case there is a save awarded, the save pitcher is also recorded. 

• With each finished game, the number of hits (singles, doubles, triples, and home runs) obtained by each player is also recorded. 

Design an Entity-Relationship diagram for the baseball database. For each entity show its primary key. Indicate the cardinality of each relationship. Determine if any of the entities will be a weak entity and describe the reasons. Show if the sub-entities would be mutually exclusive.