# Tuple Calculus

 Question 1
A relation $r(A,B)$ in a relational database has 1200 tuples. The attribute $A$ has integer values ranging from 6 to 20, and the attribute $B$ has integer values ranging from 1 to 20. Assume that the attributes $A$ and $B$ are independently distributed.

The estimated number of tuples in the output of $\sigma _{(A > 10)\vee(B=18)}(r)$ is ____________
 A 1200 B 205 C 15 D 820
GATE CSE 2021 SET-1   Database Management System
Question 1 Explanation:
 Question 2
Consider a database that has the relation schemas EMP(EmpId, EmpName, DepId) and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus.

Which of the above queries are safe?
 A (I) and (II) only B (I) and (III) only C (II) and (III) only D (I), (II) and (III)
GATE CSE 2017 SET-1   Database Management System
Question 2 Explanation:
 Question 3
Let R and S be relational schemes such that R={a,b,c} and S={c}. Now consider the following queries on the database:
$I.\pi _{R-S}(r)-\pi_{R-S}(\pi_{R-S}(r) \times S -\pi_{R-S,S}(r))$
$II.\{t|t\in \pi _{R-S}(r)\wedge \forall u \in s (\exists v \in r(u=v[s]\wedge t=v[R-S]))\}$
$III.\{t|t\in \pi _{R-S}(r)\wedge \forall v\in r(\exists u\in s(u=v[s]\wedge t=v[R-S]))\}$
IV. Select R.a, R.b From R,S Where R.c=S.c

Which of the above queries are equivalent?
 A I and II B I and III C II and IV D III and IV
GATE CSE 2009   Database Management System
Question 3 Explanation:
 Question 4
Which of the following tuple relational calculus expression(s) is/are equivalent to $\forall t \in r(P(t))$?
I. $\neg \exists t \in r(P(t))$
II. $\neg t \notin r(P(t))$
III. $\neg \exists t \in r(\neg P(t))$
IV. $\exists t \in r(\neg P(t))$
 A I only B II only C III only D III and IV only
GATE CSE 2008   Database Management System
Question 4 Explanation:
 Question 5
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?

 A Names of employees with a male supervisor. B Names of employees with no immediate male subordinates C Names of employees with no immediate female subordinates. D Names of employees with a female supervisor
GATE CSE 2007   Database Management System
Question 5 Explanation:
 Question 6
Which of the following relational query languages have the same expressive power?
I. Relational algebra
II. Tuple relational calculus restricted to safe expressions
III. Domain relational calculus restricted to safe expressions
 A II and III only B I and II only C I and III only D I, II and III
GATE IT 2006   Database Management System
Question 6 Explanation:
 Question 7
The relational algebra expression equivalent to the following tuple calculus expression:
$\left\{t \mid t \in r \land \left(t[A] = 10 \land t[B]=20\right)\right\}$ is
 A $\sigma_{(A=10 \lor B=20)} (r)$ B $\sigma_{(A=10)} (r) \cup \sigma_{(B=20)} (r)$ C $\sigma_{(A=10)} (r) \cap \sigma_{(B=20)} (r)$ D $\sigma_{(A=10)} (r) - \sigma_{(B=20)} (r)$
GATE CSE 1999   Database Management System
Question 7 Explanation:
 Question 8
Which of the following relational calculus expressions is not safe ?
 A A B B C C D D
GATE CSE 2001   Database Management System
Question 8 Explanation:
There are 8 questions to complete.

### 3 thoughts on “Tuple Calculus”

1. In tuple calculas, 3rd query is wrong it is equal to instead of not equal to.