Consider a selection of the form σ_A ≤ 100(r), where r is a relation with 1000 tuples. Assume that the attribute values for A among the tuples are uniformly distributed in the interval [ 0, 500 ]. Which one of the following options is the best estimate of the number of tuples returned by the given selection query?

Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under consideration. What does the following Tuple Relational Calculus query produce?

$$\eqalign{ & \{ e.name\,|\,employee(e) \wedge \cr & (\forall x)[\neg employee(x) \vee \cr & x.\sup ervisorName \ne e.name\, \vee \cr & x.sex = 'male']\} \cr} $$

Information about a collection of students is given by the relation studInfo(studId, name, sex). The relation enroll(studId, courseId) gives which student has enrolled for (or taken) what course(s). Assume that every course is taken by at least one male and at least one female student. What does the following relational algebra expression represent?

$$\eqalign{ & \prod\nolimits_{courseId} {((\prod\nolimits_{studId} {({\sigma _{sex = 'female'}}} } \cr & (studInfo)) \times \prod\nolimits_{courseId} {(enroll)) - enroll)} \cr} $$

Consider the table employee(empId, name, department, salary) and the two queries Q₁, Q₂ below. Assuming that department 5 has more than one employee, and we want to find the employees who get higher salary than anyone in the department 5, which one of the statements is TRUE for any arbitrary employee table?

Q1:
Select e.empId 
From employee e 
Where not exists 
  (Select * From employee s
   where s.department = "5" and 
   s.salary >=e.salary);

Q2:
Select e.empId 
From employee e 
Where e.salary > Any 
( Select distinct salary 
From employee s 
Where s.department = "5");