You are given the following database

Please write the following queries for this database utilizing relational algebra and explain your answers, thank you!

- BOOK(isbn, title, num-pages, publisher, year, genre, price, aut-id). The first attribute is the primary key; the last one is a foreign key to AUTHOR. 1 - CUSTOMER (customer-id, name, address, city, state, zip, age). The first attribute is the primary key. - SALES(isbn, custid, num-copies, day, month, year, total). The first attribute is a foreign key to BOOK and the second a foreign key to CUSTOMER. The key of this table is the two foreign keys together. - AUTHOR (author-id, name, dob, nationality, address, city, state, zip). The first attribute is the primary key. Attribute dob stands for 'date of birth'. Attribute nationality has values like 'British', 'Australian', etc. Attribute genre has values like 'sci-fi', 'romance', etc. Note that this schema assumes that each book has one and only one author, but it can be sold to different customers at different times. Write the following queries in Relational Algebra: 1. List the title and publisher of all the books that have sold at least 100 copies at any time. 2. List the title and publisher of all the books that have been sold to a customer from the state of Kentucky. 3. Find the name and address of British authors who have written a sci-fi book (recall that 'sci-fi' is one value of genre). 4. List the name and address of authors who have written either a sci-fi book or a romance book (recall that 'sci-fi' and 'romance' are values of genre). 5. List the name and address of authors who have written a sci-fi book and a romance book. 6. List the name and address of authors who have never written a sci-fi book. 7. List the name and address of authors who have written at least two books. 8. List the name and address of authors who have written only sci-fi books (i.e. all the books they have written are sci-fi)