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

Concept:
Relational calculus is a non -procedural query language. It is of two types: tuple and domain relational calculus.
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.

A = 10 and C = 7

Output:

Therefore, sum = 10 + 7 + 13 + 2 = 32

Concept:
In tuple relational calculus, there exists two quantifiers, namely universal quantifier and existential quantifier. For these, there are two types of variables: free variable and bound variable.

• 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 ∈ department (t [dept_name] = s [dept_name])
According to above rules:
t is the free variable and s is the bound variable.

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

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.