For this question, consider the five relation schemas with the primary key underlined:

artist $($id$,$ name, status$)$

work $($id$,$ name, work$\_$type, price$)$

gallery $($id$,$ name, location$)$

exhibition $($id$,$ gallery$\_$id$,$ start$\_$date, end$\_$date$)$

transaction $($id$,$ buyer, work$\_$id$,$ date, price, status$)$

The attributes in artist mean the following: id is a unique identifier for an artist; name is the name of the artist, and status takes two values, $$active$$ or $$inactive$.$

The attributes in work mean the following: id is a unique identifier assigned to the work of art $($not the artist$)$; name is the name of the work such as $$Mona Lisa$$; work$\_$type is the type of work such as painting, sculpture, photograph, etc.; and price is the appraised price of the work of art.

The attributes in the gallery table are as follows: id serves as a unique identifier for each gallery; name is the name of the gallery; location is the physical location of the gallery.

In the exhibition table, id is a unique identifier for each exhibition. gallery$\_$id is a foreign key that refers to the id in the gallery table and indicates which gallery is hosting the exhibition. start$\_$date and end$\_$date indicate the duration of the exhibition.

In the transaction table, id is a unique identifier for each transaction involving the sale of a work of art. buyer is the name of the individual or entity purchasing the work. work$\_$id is a foreign key that refers to the id in the work table and identifies which piece of art is being sold, purchased, or refunded. Thus, it can hold a negative value in the price attribute. date is the date the transaction occurred, and price is the selling price of the artwork

a$.[20$ points$]$ For this question, assume that a single artist creates a work of art but can create many works of art, and each artist may have none, one or more works of art. Modify the artist and$/$or work relation$($s$),$ possibly adding a third relation, if necessary, so that two tables can be properly joined together. For this question, provide answers to the following questions using the notation$/$diagrams explained in class. All relations should be provided and primary keys, foreign keys and relationships properly presented in the database schema$/$diagram$.$

$($i$)$ The potentially modified relation schemas for artist and work and, if necessary, a third relation schema with the primary key underlined in each relation schema.

$($ii$)$ The relational diagram for your relations with the arrows appropriately representing the foreign keys.

$($iii$)$ The Entity$-$Relationship Diagram using Crow$$s Foot diagram notation for your modified relations.

$($iv$)$ The Entity$-$Relationship Diagram using Chen$$s diagram notation for your modified relations

b$.[20$ points$]$ For this question, assume one or more than one artist can create a work of art or many works of art. Note also, as above, that an artist may not have created any work of art. Modify the artist and$/$or work relation$($s$),$ possibly adding a third relation, if necessary, so that two tables can be properly joined together. For this question, provide answers to the following questions using the notation$/$diagrams explained in class. All relations should be provided and primary keys, foreign keys and relationships properly presented in the database schema$/$diagram$.$

$($i$)$ The potentially modified relation schemas for artist and work and if necessary a third relation schema with the primary key underlined in each relation schema.

$($ii$)$ The relational diagram for your relations with the arrows appropriately representing the foreign keys.

$($iii$)$ The Entity$-$Relationship Diagram using Crow$$s Foot diagram notation for your modified relations.

$($iv$)$ The Entity$-$Relationship Diagram using Chen$$s diagram notation for your modified relations.

c$.[20$ points$]$ For this question, assume that one or more artists can create a work of art, or many works of art. Note also, as above, that an artist may not have created any work of art. In addition, galleries host exhibitions featuring works of art, and transactions for these works occur over time. Modify the artist, work, gallery, exhibition, and transaction relations, possibly adding additional relations if necessary, so that the tables can be properly joined together.

$($i$)$ Provide potentially modified relation schemas for artist, work, gallery, exhibition, and transaction, and add any necessary new relation schemas with the primary key underlined in each relation schema.

$($ii$)$ Create a relational diagram with arrows appropriately representing the foreign keys across all tables.

$($iii$)$ Develop an Entity$-$Relationship Diagram using Crow$$s Foot diagram notation for your modified relations.

$($iv$)$ Create an Entity$-$Relationship Diagram using Chen$$s diagram notation for your modified relations.