Part $2$

Problem $1(10$ Points$)$:

Draw the relational algebra tree for the following query:

${}_{\text{S}\text{i}\text{d}\text{,}\text{C}\text{i}\text{d}}((({}_{\text{S}\text{i}\text{d}\text{,}\text{S}\text{n}\text{a}\text{m}\text{e}\text{,}\text{M}\text{a}\text{j}\text{o}\text{r}}({}_{\text{G}\text{p}\text{a}}>3\mathrm{.}4($ Student $)))|><mi>|</mi>$ Enroll Course $))))$

Problem $2(10$ Points$)$:

Show how to derive the following equivalence by a sequence of transformations using the equivalence rules. Your

solution must include the step$-$by$-$step procedure with the rule specified in each step.

where ${}_2$ involves only attributes of $E_2$

Problem $3(30$ Points$)$:

Consider a relation Student$($Sid$,$ Sname, Major, Status, Gpa$)$ with $20,000$ tuples. Assume there are $100$ different

values of Major, $5$ different values of Status, and Gpa values are between $0\mathrm{.}00$ and $4\mathrm{.}00($Gpa is calculated with $2$

decimal positions$).$ Show your steps to estimate the number of tuples selected in each of the following queries. No

point is given if only the answer is provided.

$($a$)$ Student