GATE CS 2012 Q.50 (CS Q.50): Relational Algebra and Tuple Relational Calculus

Common data questions

Common Data for Questions 50 and 51:

Consider the following relations A, B and C:

Relation A:

Id	Name	Age
12	Arun	60
15	Shreya	24
99	Rohit	11

Relation B:

Id	Name	Age
15	Shreya	24
25	Hari	40
98	Rohit	20
99	Rohit	11

Relation C:

Id	Phone	Area
10	2200	02
99	2100	01

Shared with question 51.

How many tuples does the result of the following relational algebra expression contain? Assume that the schema of $A \cup B$ is the same as that of $A$ .

(A \cup B) \bowtie_{A.\text{Id} > 40 \lor C.\text{Id} < 15} C

Official answer and solution

Official answer: A
From: Official GATE 2012 answer key

Solution

Compute the relation union A U B, then evaluate the theta-join condition (A.Id > 40 OR C.Id < 15) with relation C.

Relation union $A \cup B$ (set union removes duplicate rows):

Tuples in $A$ : (12, Arun, 60), (15, Shreya, 24), (99, Rohit, 11)
Tuples in $B$ : (15, Shreya, 24), (25, Hari, 40), (98, Rohit, 20), (99, Rohit, 11)
Distinct tuples in $A \cup B$ $A \cup B$ (5 tuples):
1. (12, Arun, 60)
2. (15, Shreya, 24)
3. (25, Hari, 40)
4. (98, Rohit, 20)
5. (99, Rohit, 11)

Relation $C$ contains 2 tuples:

$c_1 = (10, 2200, 02)$ with $\text{Id} = 10$
$c_2 = (99, 2100, 01)$ with $\text{Id} = 99$

Evaluating join condition $(A.\text{Id} > 40) \lor (C.\text{Id} < 15)$ for each pair:

For tuple $c_1$ ( $C.\text{Id} = 10$ ): Since $10 < 15$ is TRUE, the disjunction is TRUE for all 5 tuples of $A \cup B$ . Yields 5 tuples.
For tuple $c_2$ ( $C.\text{Id} = 99$ ): $C.\text{Id} < 15$ is FALSE. The condition holds only if $A.\text{Id} > 40$ . In $A \cup B$ , tuples with $\text{Id} > 40$ are (98, Rohit, 20) and (99, Rohit, 11). Yields 2 tuples.

Total result tuples:

\text{Total tuples} = 5 + 2 = 7

This matches option (A).

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2012 Computer Science and Information Technology (CS)
Question: 50 of 65, printed as CS Q.50
Section: Computer Science and Information Technology

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