The document describes two database design exercises. The first involves designing a database to store information about employees, departments, and employee children. It involves entities for employees, departments, and children and relationships indicating employees work in departments, departments have managers, and children can be identified through their parent employee. The second exercise involves designing a database for an art gallery. It involves entities for artists, artworks, groups, and customers. Artworks are created by artists and can belong to multiple groups. Customers like certain artists and groups. The solution diagrams the entities and relationships along with constraints like each artwork is created by one artist.