Query $27$: For each project, retrieve the project number, the project name, and the number of employees from department $5$ who work on the project.

SELECT Pnumber, Pname, COUNT $(*)$

FROM PROJECT, WORKS$\_$ON$,$ EMPLOYEE

WHERE Pnumber $=$ Pno AND Ssn $=$ Essn AND Dno $=5$

GROUP BY Pnumber, Pname;

a$.$ Draw at least two equivalent query trees $($using Relational Algebra$)$ that can represent the query. $[5$ points$]$

b$.$ Draw the initial query tree, in its canonical form, for the query, and then show and discuss how the query tree can be optimized using pipelining. $[10$ points$]$

c$.$ Apply pipelining to the query trees drawn in part $($a$),$ compare them with the initial query tree in part $($b$).$ Which query trees benefits the most from pipelining? $[10$ points$]$