Consider a hash function that distributes keys uniformly. The hash table size is 20. After hashing of how many keys will the probability that any new key hashed collides with an existing one exceed 0.5.

Which one of the following statements if FALSE?

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");

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?

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