Problem 1. (80 points) Consider the relational database defined below: create table professor ( professor_ID varchar ( 1 0 ) , professor_name varchar ( 3 0 ) , ZIP_code char ( 5 ) , salary numeric (10 , 2 ) , primary key ( professor_ID ) ) ;

create table student ( student_ID varchar ( 1 0 ) , student_name varchar ( 3 0 ) , ZIP_code char ( 5 ) , primary key ( student_ID ) ) ;

create table advisement ( professor_ID varchar ( 1 0 ) , student_ID varchar ( 1 0 ) , start_date date , primary key ( professor_ID , student_ID ) , foreign key ( professor_ID ) references professor , foreign key ( student_ID ) references student ) ;

Express in SQL each of the following queries: (e) (10 points) Find the IDs of the professors not advising any student (use a left outer join and is null).

(f) (10 points) Find the ID of each student advised by SOME of the professors who advise student S001 (i.e., student whose ID is S001).

(g) (10 points) Find the ID of each student advised by ALL of the professors who advise student S001 (i.e., student whose ID is S001).

(h) (10 points) Find the ID(s) of the professor(s) that advise the largest number of students.