Test: Tuple Calculus - Computer Science Engineering (CSE) MCQ

There are two 'there exists' clauses in the given tuple relational calculus which are connected by and (ᴧ). The tuple variable u is restricted to departments that are located in the Taylor building, while tuple variable s is restricted to instructors whose dept_name matches that of tuple variable u.

Therefore, the given expression finds the names of all instructors whose department is in the Taylor building.

Query 1:
It is a Tuple relational calculus query first comparing all tuples with the city is equal to Hyd in deposit table and fetch the customer name when  city="Hyd".

Query 2:
It is a Domain relational calculus query first comparing city domain with city equal to Hyd in deposit table and fetch the customer name when city="Hyd".

Query 3:
It is a relational algebra query, In the first step fetch all names whose city hyd in the branch table. And the second step joining the deposit and branch and comparing the city equal to 'Hyd' with fetching city_name and branch_name. Finally, division step 2 with step1 will results in customers having account all branches located in Hyderabad.

Hence the correct answer is all the above are giving the same result.

The condition EMPLOYEE(t) specifies that the range relation of tuple variable t is EMPLOYEE. First name and last name of EMPLOYEE tuple t that satisfies the condition t.Salary > 15000 will be retrieved.

{t.Fname, t.Lname | EMPLOYEE(t) AND t.Salary > 15000} is the correct expression.

• A tuple variable t is bound if it is quantified, meaning that it appears in existential or universal quantifier clause, otherwise it is free. Formally, tuple variable is free or bound as :
• An occurrence of a tuple variable in a formula F that is an atom is free in F.
• An occurrence of a tuple variable t is free or bound in a formula made up of logical connectives – (F1 AND F2), (F1 OR F2), NOT(F1) and NOT(F2)- depending on whether it is free or bound in F1 or F2. In a formula of the form F = (F1 AND F2) or F = (F1 OR F2), a tuple variable may be free in F1 and bound in F2 or vice versa.
• All free occurrences of a tuple variable t in F are bound in F’ of form F’ = (∃ t) F or F’ = (for all t)F

Here, given expression is :
t ϵ instructor ∧ ∃ s ϵ department (t [dept_name] = s [dept_name])

According to above rules:
t is the free variable and s is the bound variable.

Tuple relational calculus is to select the tuples. It is represented by:
{T | P(T)}
P(T) is condition to fetch the tuple T.

Example:
{T.name| Author(T) AND T.book = ‘Operating system’}
It selects the tuple having author of book Operating system.

Every query that can be expressed using a safe relational calculus query can also be expressed as a relational algebra query.
Therefore, relation algebra has the same power as safe relational calculus
Option 4 is correct

Confusion Points:
Relational algebra is not having same power as relational calculus unless it is safe relational calculus

Option 1: {t, c, f | ∃f ϵ COLLEGE(t[FacultyName] = f[FacultyName] ∩ ∃c ϵ COLLEGE(c[CollegeID] = f[CollegeID] ∩ c[Name] = “TESTBOOK”))}
This Query is not correct. Since this Query will return facultyName, collegeID, and facultyName.

Option 2: {t | ∃f ϵ FACULTY(t[FacultyName] = f[FacultyName] ∩ ∃c ϵ COLLEGE(c[FacultyName] = f[CollegeID] ∩ c[Name] = “TESTBOOK”))}
This Query is not correct. because there is no attribute name FacultyName in COLLEGE relation ( since ∃c ϵ COLLEGE).

Option 3: {t, c, f | ∃f ϵ FACULTY(t[FacultyName] = f[FacultyName] ∩ ∃c ϵ COLLEGE(c[CollegeID] = f[CollegeID] ∩ c[Name] = “TESTBOOK”))}
This Query is not correct. Since this Query will return facultyName, collegeID, and facultyName.

Option 4: {t| ∃f ϵ FACULTY(t[FacultyName] = f[FacultyName] ∩ ∃c ϵ COLLEGE(c[CollegeID] = f[CollegeID] ∩ c[Name] = “TESTBOOK”))}
This Query is correct.

Tuple − A single row of a table, which contains a single record for that relation is called a tuple.

The question asks for the type of relational calculus that uses domain variables that take on values from an attribute's domain, rather than values for an entire tuple.
From the explanations:

Tuple Relational Calculus (TRC) uses tuple variables, not domain variables.
Relational Algebra operates on entire relations and does not use domain variables.
Domain Relational Calculus (DRC) specifically uses domain variables that take on values from an attribute’s domain.
Thus, the correct answer is:

C: Domain relational calculus