Given that the following schema and SQL query:

Schema

STUDENT$($sid $,$ fullName, DoB, email$)$

STUDIES$\_$ON$($stid$,$ ctid$)$

COLLEGE$($cid$,$ cName$)$

SQL Query

SELECT fullName

FROM STUDENT,

SUTDIES$\_$ON$,$

COLLEGE

WHERE sid $=$ stid

AND ctid $=$ cid

AND cName $=$ 'CCI';

a$)$ Convert the query above into Relational Algebra expression.

b$)$ Draw the initial query tree of the query.

c$)$ Write the rule and show how the query tree is optimized after applying Heuristic Rules Optimization in each step.