Question 35

The English specification is: "Find the distinct names of all students who score more than 90% in the course numbered 107".

Let us evaluate each query representation:

• (I) SQL Query:

  SELECT DISTINCT S.sname
  FROM Students as S, Registration as R
  WHERE R.rollno=S.rollno AND R.courseno=107 AND R.percent > 90
  

  This correctly joins Students and Registration on rollno, applies the filters courseno = 107 and percent > 90, and returns distinct student names (sname). This is equivalent.

• (II) Relational Algebra Expression:

  $$\Pi_{\text{sname}}(\sigma_{\text{courseno}=107 \land \text{percent}>90}(\text{Registration} \bowtie \text{Students}))$$

  The natural join automatically joins on common attribute rollno. Selection filters rows where courseno = 107 and percent > 90. Projection $\Pi$ in relational algebra inherently eliminates duplicates. This is equivalent.

• (III) Tuple Relational Calculus (TRC):

  $$\{T \mid \exists S \in \text{Students}, \exists R \in \text{Registration} (S.\text{rollno}=R.\text{rollno} \land R.\text{courseno}=107 \land R.\text{percent}>90 \land T.\text{sname}=S.\text{sname})\}$$

  This specifies tuples $T$ with attribute sname belonging to students registered for course 107 with percent exceeding 90. Set semantics guarantees distinct results. This is equivalent.

• (IV) Domain Relational Calculus (DRC):

  $$\{\langle SN \rangle \mid \exists SR, \exists RP (\langle SR, SN \rangle \in \text{Students} \land \langle SR, 107, RP \rangle \in \text{Registration} \land RP > 90)\}$$

  Here $SN$ is the domain variable for student name, $SR$ represents rollno, and $RP$ represents percent. The conditions check existence of matching tuples in Students and Registration where course is 107 and percent is greater than 90. Set semantics ensures distinct values of $SN$. This is equivalent.

All four queries (I, II, III, and IV) are equivalent to the English query. Therefore, option (A) is correct.