GATE Computer Science (CS) 2013 Solved Paper

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”
(I) SELECT DISTINCT S.sname
FROM Students as S, Registration as R
WHERE R.rollno=S.rollno AND R.courseno=107 AND R.percent >90
(II) Π_sname (σ_{courseno = 107∧percent>90} (Registration ⋈ Students))
(III) {T | ∃S ∈ Students, ∃R ∈ Registration (S.rollno = R.rollno ∧R. courseno = 107 ∧ R.percent > 90 ∧ T.sname = S. sname)}
(IV) {〈S_N〉 | ∃S_R∃R_P(〈S_R, S_N〉 ∈ Students ∧ 〈S_R, 107, R_P〉 ∈ Registration ∧ R_P > 90)}