title: SQL double negation with Not exists
body: <p>I have a nested Not Exists, and was wondering if its a double negation. And if I remove both the negation, if it would be the equivalent queries? </p>
  
  <pre><code>Suppliers(sid: integer, sname: string, address: string)
  Parts(pid: integer, pname: string, color: string)
  Catalog(sid: integer, pid: integer, cost: real)
  </code></pre>
  
  <p>SQL Translation :  "C.Sid for which Does not exist the parts that are not supplied by C.Sid"</p>
  
  <pre><code>SELECT C.sid
  FROM Catalog C
  WHERE NOT EXISTS (SELECT P.pid
                    FROM Parts P
                    WHERE NOT EXISTS (SELECT C1.sid
                                      FROM Catalog C1
                                      WHERE C1.sid = C.sid
                                      AND C1.pid = P.pid)
                    )
  </code></pre>
  
  <p>Removed Negations : "C.Sid who supply every part"</p>
  
  <pre><code>SELECT C.sid
  FROM Catalog C
  WHERE EXISTS (SELECT P.pid
                    FROM Parts P
                    WHERE EXISTS (SELECT C1.sid
                                      FROM Catalog C1
                                      WHERE C1.sid = C.sid
                                      AND C1.pid = P.pid)
                    )
  </code></pre>