Consider the following relational database schema $S,$

$)))$

and the following SQL query:select distinct tutor.name$$from $($staff join teach on $($staff$.$uid $=$ teach.uid$))$ as tutor,$($staff join teach on $($staff$.$uid $=$ teach.uid$))$ as convener,$$course$$where tutor.ccode $=$ convener.ccode$$and tutor.sem $=$ convener.sem$$and tutor.year $=$ convener.year$$and convener.role $=$ 'convener'$$and tutor.role $=$ 'tutor'$$and convener.ccode $=$ course.ccode$$and convener.name $=$ 'Graham'$$and course.level $=2000$;

$1.$ Translate the above query into a relational algebra query, using only the operators in the table above. You may use relational algebra expressions to represent intermediate results if needed.

$2$ Draw the query tree for the relational algebra query you constructed for question $(1).$

$3$ Optimise the relational algebra query.