To solve the query question, we need to select the names of students enrolled in the course with course number 1470. We have the following relation schemas:

• Students (rollno: integer, name: string, age: integer, cgpa: real)
• Courses (courseno: integer, cname: string, credits: integer)
• Enrolled (rollno: integer, courseno: integer, grade: string)

The task requires us to retrieve student names, hence we look at the Students and Enrolled tables. The key here is to match students’ roll numbers who are listed as enrolled in the specified course.

Let's analyze the options provided:

1. Option 1:    SELECT S.name    FROM Students S    WHERE EXISTS (      SELECT *      FROM Enrolled E      WHERE E.courseno = 1470      AND E.rollno = S.rollno    );    

This query correctly identifies students enrolled in the course number 1470 by using the EXISTS clause to check if the student's roll number is present in the Enrolled table for the given course. This approach is valid and efficient.

1. Option 2:    SELECT S.name    FROM Students S    WHERE SIZEOF (      SELECT *      FROM Enrolled E      WHERE E.courseno = 1470      AND E.rollno = S.rollno    ) > 0;    

This option is incorrect. In standard SQL, there is no SIZEOF function. Thus, this query is invalid due to using a non-existing SQL function.

1. Option 3:    SELECT S.name    FROM Students S    WHERE 0 < (      SELECT COUNT(*)      FROM Enrolled E      WHERE E.courseno = 1470      AND E.rollno = S.rollno    );    

This query is also correct. It uses a subquery that counts the number of records in the Enrolled table where the course number is 1470 and student roll numbers match. The condition 0 < ensures that we get only those students who have at least one matching record in Enrolled.

1. Option 4:    SELECT S.name NATURAL JOIN Enrolled E    FROM Students S E    WHERE E.courseno = 1470;    

This option is incorrect. The use of NATURAL JOIN syntax in this context is incorrect or incomplete, leading to syntax errors and incorrect query logic.

Conclusion: Based on the syntax and logical structure required for this query, Option 1 and Option 3 are correct choices. They appropriately filter students based on their enrollment in the specified course and retrieve the required names.