# GATE | GATE CS 2013 | Question 65

Consider the following relational schema.

Students(rollno: integer, sname: string) Courses(courseno: integer, cname: string) Registration(rollno: integer, courseno: integer, percent: real)

Which of the following queries are equivalent to this query in English?

"Find the distinct names of all students who score more than 90% in the course numbered 107"

**(A)** I, II, III and IV**(B)** I, II and III only**(C)** I, II and IV only**(D)** II, III and IV only**Answer:** **(A)****Explanation:**

Option A: This is a SQL query expression. It first perform a cross product of Students and Registration, then WHERE clause only keeps those rows in the cross product set where the student is registered for course no 107, and percentage is > 90. Then select distinct statement gives the distinct names of those students as the result set.

Option B: This is a relational algebra expression. It first perform a NATURAL JOIN of Students and Registration (NATURAL JOIN implicitly joins on the basis of common attribute, which here is rollno ), then the select operation( sigma) keeps only those rows where the student is registered for courseno 107, and percentage is > 90. And then the projection operation (pi) projects only distinct student names from the set. Note: Projection operation (pi) always gives the distinct result.

Option C: This is a Tuple Relational Calculus (TRC) language expression, It is not a procedural language (i.e. it only tells “what to do”, not “how to do”). It just represents a declarative mathematical expression. Here T is a Tuple variable. From left to right, it can be read like this, “It is a set of tuples T, where, there exists a tuple S in Relation Students, and there exist a tuple R in relation Registration, such that S.rollno = R.rollno AND R.couseno = 107 AND R.percent > 90 AND T.sname = S.sname”. And the schema of this result is (sname), i.e. each tuple T will contain only student name, because only T.sname has been defined in the expression. As TRC is a mathematical expression, hence it is expected to give only distinct result set.

Option D: This is a Domain Relational Calculus (DRC) language expression. This is also not procedural. Here SN is a Domain Variable. It can be read from left to right like this “The set of domain variable SN, where, there exist a domain variable SR , and a domain variable Rp, such that, SN and SR domain variables is in relation Students and SR,107,RP is a domain variables set in relation Registration, AND RP > 90 “ Above, SN represents sname domain attribute in Students relation, SR represents rollno domain attribute in Students relation, and RP represents percentage domain attribute in Registration relation. The schema for the result set is (SN), i.e. only student name. As DRC is a mathematical expression, hence it is expected to give only distinct result set.