GATE Computer Science Engineering(CSE) 2027 Test: Relational Algebra, Tuple

The given query
SELECT DISTINCT W, X
FROM R, S
Is guaranteed to be same as R, if R has no duplicates and ‘S’ is non-empty.
Since, if R is having a duplicates, then the tuples selected by SELECT operation of the R and the given query will not be same also if ‘S’ is empty then the given query outputs null.

From the relation DEPOSIT first we have to select the those entries in which balance is over 1000. This can be obtained by  (Deposit), Now, we have to select those customers name who have balance over 1000 which can be obtained by simply projecting customer name in above subquery.

Clients of Bankers Agassi can be obtained by using the relation client_scheme while the corresponding customer_city can be obtained -using customer_scheme.
Hence cross product of client and customer must be taken. This can be achieved in two ways.
(i) First taking the Bankers Agassi clients and then checking their name in customer relation and projecting their customer city.
(ii) First taking all the customers and matching them in customer_scheme, then finding out the customers who have the Agassi as the Banker, finally projecting the customer_city of the respective customers.

We have to find all customers in the relation Borrow, this can be achieved by
 borrow (t [custome _name ])=s [customer_name]
The s here is bound variable and the condition of checking Ioan-amount more than 1200 is to be checked with each customer name condition.

All customers who have a lone amount of over 1200

The WHERE condition checks for the Grade = ‘A' and matching of course-number in the courses and Grades, where the instructor must be ‘Korth’. Overall it checks for students to whom ‘Korth’ has instructed and they have received Grade = ‘A in atleast one of the courses taught by ‘Korth’.

Determining the Maximum and Minimum Number of Tuples in the Natural Join of Student and Enroll Tables
Step 1: Understanding the Given Tables
Student Table: Contains 120 tuples with attributes rollno, name, and address. The primary key is rollno.
Enroll Table: Contains 8 tuples with attributes rollno, courseno, and coursename. The primary key is a combination of rollno and courseno.

Step 2: Concept of Natural Join
A natural join between Student and Enroll will match tuples based on the common attribute rollno. This means:

Only those tuples from Student that have a matching rollno in Enroll will appear in the result.
The number of tuples in the resulting table depends on how rollno values are distributed between both tables.

Step 3: Finding the Maximum Number of Tuples
The maximum number of tuples occurs when each tuple in the Enroll table has a matching rollno in the Student table.
Since Enroll has only 8 tuples, the maximum number of tuples in the join is 8.

Step 4: Finding the Minimum Number of Tuples
The minimum number of tuples occurs when all rollno values in Enroll match the same single rollno in Student.
Even in this case, all 8 tuples from Enroll will be present in the join result (since each enroll record must have a matching student).
Therefore, the minimum number of tuples is also 8.

Final Answer:
Maximum number of tuples = 8
Minimum number of tuples = 8
Thus, the correct answer is:
8, 8.

The given query first calculates the average salary from the relation Employee, then it selects the department name where employees who have average salary more than the average salary of the company.

Relation algebra is procedural query language while relational calculus is non-procedural query language.

The condition T. assets > S. assets and S. branch_city = “PONDICHERRY” checks for the all those branch-name who have greater assets than any branch located in Pondicherry. The keyword distinct removes the duplicacy of branch_name satisfy the given condition.

All of the given option valid:

They simply find and selects the tuples which are common to both P and Q.

The conditions c₁ and c₂ may not be same.

Find the customers who appears in r₂ with every branch name in r₁
So, it is represented by division query: 

With the help of {π, x, -} we can perform division operation.
Note: Division operator produces a relation R(X) that includes all tuples t[x] in R(z) that appear in R in combination with every tuple from R₂y) when Z = X ∪ Y.

A relational calculus expression may contain infinite tuples that are not in the relation, R₁.

Hence, the above expression is not safe.