Q$2$ Consider the following SQL query

SELECT E$.$Lname AS Employee$\_$name, S$.$Lname AS Supervisor$\_$name

FROM EMPLOYEE AS E$,$ EMPLOYEE AS S

WHERE E$.$Super$\_$ssn$=$S$.$Ssn;

$($a$)$ Draw at least two query trees that can represented each of that query.

Under what circumstances would you use each of your query trees?

$($b$)$ Draw the initial query tree for each of that query; then show how the

query tree is optimized by the algorithm outlined in section $19\mathrm{.}7.$

$($c$)$ Compare your on$-$query trees of part $($a$)$ and the initial and

final query trees of part $($b$).$