Which of the following scenarios may lead to an irrecoverable error in a database system?

Consider the following SQL query:

Select distinct a1, a2, ..., an 

From r1, r2, ..., rm 

Where P; 

For an arbitrary predicate P, this query is equivalent to which of the following relational algebra expressions?

Consider the set of relations shown below and the SQL query that follows.

Students: (Roll_number, Name, Date_of_birth)
Courses: (Course number, Course_name, Instructor)
Grades: (Roll_number, Course_number, Grade)

Select distinct Name
From Students, Courses, Grades
Where Students.Roll_number = Grades.Roll_number
      and Courses.Instructor = 'Korth'
      and Courses.Course_number = Grades.Course_number
      and Grades.grade = 'A';

Which of the following sets is computed by the above query?

Consider the following functional dependencies in a database.
$$\eqalign{ & \,\,\,\,Date\,\,of\,\,Birth\,\, \to \,\,Age \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Age\,\, \to \,\,Eligibility \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Name\,\, \to \,\,Roll\_number \cr & \,\,\,\,\,Roll\_number\,\, \to \,\,Name \cr & Course\_number\, \to \,\,Course\_name \cr & Course\_number\, \to Instructor \cr & (Roll\_Number,\,Course\_number)\,\, \to \,\,Grade \cr} $$

The relation (Roll_number, Name, Date_of_Birth, Age) is