Use the database schema of Question 1 to write OPTIMIZED relational algebra for the following queries: 1) List the name of all managers who do not have The Little Prince in their libraries. ("The Little Prince" is a book name) 2) Borrowers should like their favorite book. List the name of all borrowers who DO NOT like their favorite book. 3) List the name of the libraries whose managers live in lake Charles. 4) List the name of managers whose libraries loan book genre "science fiction". 5) List phone numbers that are recorded both for the library and the manager phone. 6) List name of managers who live in the same city that Mr. "Mark" (name of one of the managers) lives. Question 3 (10 marks): Consider the following schema, query, and relational algebra expression: student (id, name) enrolledIn (id, code) subject (code, lecturer) Query: What are the names of students who are either in CMPS 460 or in CMPS 340? Relational algebra expression: Iname ((6 code='CMPS460' (student enrolled In)) U (6 code='CMPS340' (student enrolledIn))) Optimize the above relational algebra expression.