SQL

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) $\Pi_{sname}(\sigma_{courseno=107 \land percent>90}(\text{Registration} \bowtie \text{Students}))$ (III) $\{T \mid \exists S \in \text{Students}, \exists R \in \text{Registration}\ (S.rollno = R.rollno \land R.courseno = 107 \land R.percent > 90 \land T.sname = S.sname)\}$ (IV) $\{\langle S_N \rangle \mid \exists S_R \exists R_P\ (\langle S_R, S_N \rangle \in \text{Students} \land \langle S_R, 107, R_P \rangle \in \text{Registration} \land R_P > 90)\}$