title: Relational Algebra check for error
body: <p><strong>Hi could someone please verify my work. Im not sure if im doing any of this correctly and would greatly appreciate any help. I am not allow to use the Bow tie operator. Thank you.</strong></p>
  
  <p><strong>Question:</strong></p>
  
  <pre><code>Books (ISBN, Title, Authors, Publisher, Ed, Year, Genre)
  Patron (MemberNumber, FirstName, LastName, AddressLn1, AddressLn2, City, State, Zipcode)
  Loan (MemberNumber,ISBN,DateLoaned,DateDue, DateReturned)
  
  Business Logic
  •   You may assume that the library only has one copy of each book.  
  •   Each book may have many authors.  If a particular book has multiple authors, they are listed as a comma separated string.  You may assume that the same author always uses the same exact name and no two authors will have the same name.
  •   Year is stored as an integer.
  •   DateLoaned, DateDue, and DateReturned are stored as a date.
  •   When a book is initially lent out, DateReturned is set to be NULL, upon its return, the value is updated.
  
  1.1.    Find all books that were loaned out after 12/22/2012.  Show the ISBN, Title, and DateDue.
  1.2.    Find all library patrons who have borrowed a book titled "Database Systems".  Show their FirstName, LastName, and DateLoaned.
  1.3.    Find all books that were ever loaned out.  Display the ISBN.
  1.4.    Find all books returned before 12/22/2012.   Display the ISBN.
  1.5.    Find all books returned on or after 12/22/2012.  Display the ISBN.
  1.6.    Find all books returned either (before 12/22/2012) or (on or after 12/22/2012)  Display the ISBN.
  1.7.    In 1 sentence explain the difference between 1.3 and 1.6.
  1.8.    Find all patrons who have never borrowed a book. 
  1.9.    Find all books with Genre "Mystery" that have NEVER been loaned out.
  1.10.   Create a new attribute ImportantDates.  A date is important if it is in the Loan relation either as a DateLoaned or a DateDue.  Display ImportantDates.
  1.11.   Find all library patrons who have borrowed a book with an author "James Stewart".  You may use the expression LIKE "%James Stewart%" in your Relational Algebra.
  1.12.   Find all library patrons who have never borrowed a book with an author "James Stewart".  You may use the expression LIKE "%James Stewart%" in your Relational Algebra.
  1.13.   Find all library patrons who have only borrowed a book with an author "James Stewart".  If they have ever borrowed a book without the author "James Stewart" they should be excluded.  You may use the expression LIKE "%James Stewart%" in your Relational Algebra. 
  </code></pre>
  
  <p><strong>Answer:</strong></p>
  
  <pre><code>1.1) πISBN,TITLE,DATEDUE(σDATELOANED &gt; 12222012 AND BOOKS.ISBN = LOAN.ISBN(LOAN X BOOKS)
  1.2) πFIRSTNAME,LASTNAME,DATELOANED(σTITLE = "DATABASE SYSTEMS" AND BOOKS.ISBN = LOAN.ISBN AND PATRON.MEMBERNUMBER = LOAN.MEMBERNUMBER(BOOKS X PATRON X LOAN))
  1.3) πISBN(σDATELOANED &lt;&gt; "NULL" AND BOOK.ISBN = LOAN.ISBN(LOAN X BOOKS))
  1.4) πISBN(σDATELOANED &lt; 12222012 AND BOOK.ISBN = LOAN.ISBN(LOAN X BOOKS))
  1.5) πISBN(σDATELOANED &gt;= 12222012 AND BOOK.ISBN = LOAN.ISBN(LOAN X BOOKS))
  1.6) πISBN(σDATELOANED &gt;= 12222012 OR DATELOANED &lt;12222012 AND BOOK.ISBN = LOAN.ISBN(LOAN X BOOKS))
  1.7) 1.3 AND 1.6 are the same as they both find books that have been loaned.
  1.8) σDATELOANED = "NULL" AND PATRON.MEMBERNUMBER = LOAN.MEMBERNUMBER(LOAN X PATRON)
  1.9) σGENRE = "MYSTERY" AND BOOKS.ISBN = LOAN.ISBN AND DATELOANED = "NULL"
  1.10) LOAN(DATELOANED,DATEDUE) -&gt; IMPORTANTDATE
  </code></pre>
  
  <p><strong>Could you please give me an example of either 1.11, 1.12, or 1.13 as I have no clue in how to use the LIKE expression.</strong></p>