Consider the following relational schema for a library:
Write the following queries in relational algebra.
a. Find the names of members who have borrowed any book published by "McGraw-Hill".
b. Find the name of members who have borrowed all books published by "McGraw-Hill".
c. Find the name and membership number of members who have borrowed more than five different books published by "McGraw-Hill".
d. For each publisher, find the name and membership number of members who have borrowed more than five books of that publisher.
e. Find the average number of books borrowed per member. Take into account that if an member does not borrow any books, then that member does not appear in the borrowed relation at all.