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?

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

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?

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?

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

A table ‘student’ with schema (roll, name, hostel, marks), and another table ‘hobby’ with schema (roll, hobbyname) contains records as shown below:

Table: student

Roll	Name	Hostel	Marks
1798	Manoj Rathod	7	95
2154	Soumic Banerjee	5	68
2369	Gumma Reddy	7	86
2581	Pradeep Pendse	6	92
2643	Suhas Kulkarni	5	78
2711	Nitin Kadam	8	72
2872	Kiran Vora	5	92
2926	Manoj Kunkalikar	5	94
2959	Hemant Karkhanis	7	88
3125	Rajesh Doshi	5	82

Table: hobby

Roll	Hobbyname
1798	chess
1798	music
2154	music
2369	swimming
2581	cricket
2643	chess
2643	hockey
2711	volleyball
2872	football
2926	cricket
2959	photography
3125	music
3125	chess

The following SQL query is executed on the above tables:

Select hostel
From student natural join hobby
Where marks > = 75 and roll between 2000 and 3000;

Relations S and H with the same schema as those of these two tables respectively contain the same information as tuples. A new relation S’ is obtained by the following relational algebra operation:

$$\eqalign{ & S' = \prod\nolimits_{hostel} {(({\sigma _{S.roll = H.roll}}} \cr & ({\sigma _{marks > 75\,\,\,and\,\,roll > 2000\,\,and\,\,roll < 3000}}(S))X(H)) \cr} $$

The difference between the number of rows output by the SQL statement and the number of tuples in S’ is