Consider the following schema:

employee(emp_id, first_name, last_name, department), book(isbn, title, publisher, genre), book_author(isbn, author_id), book_loan(emp_id, isbn, loan_date, return_date)

This is a database that keeps track of books borrowed by employees. The employee relation describes an employee. The book relation describes the books the company has. The book_author relation specifies the authors of the book. The book_loan relation describes the books an employee has borrowed.

Write the following queries in relational algebra.

1.Find publishers who publish both theory books and machine learning books.

2.Find the names of the employees that currently have a book checked out.

3.Find the ids of the employees who have borrowed a database book, but not a security book.

4.Find the department of each employee.

5.Find the titles of the books that are either about databases or data mining

6.Find the departments that have checked out books.