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

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.