GATE CS 2024 Set 2 — Question 45

MCQ+2 / -0.67HardSelection & ProjectionRelational ModelDatabases

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Last updated 20 August 2026

Question

The relation schema, Person(pid, city), describes the city of residence for every person uniquely identified by pid. The following relational algebra operators are available: selection, projection, cross product, and rename.

To find the list of cities where at least 3 persons reside, using the above operators, the minimum number of cross product operations that must be used is

Correct answer

(B) 2

Solution

To find cities with at least 3 persons, we need to find three distinct persons

p_1, p_2, p_3

such that they all live in the same city.
In relational algebra, this is achieved by joining the Person relation with itself. Since only cross product (Cartesian product) is available (along with selection and projection), we perform the join manually.

We need 3 instances of the Person relation, say

P_1, P_2, P_3

1.Perform

P_1 \times P_2

. This is the 1st cross product.

2.Perform

(P_1 \times P_2) \times P_3

. This is the 2nd cross product.

After obtaining

P_1 \times P_2 \times P_3

, we apply selection to ensure:

$P_1.city = P_2.city = P_3.city$
$P_1.pid \neq P_2.pid$
$P_2.pid \neq P_3.pid$
$P_1.pid \neq P_3.pid$

Finally, we apply projection to get the city.
Since we need to combine 3 tables, we require

3 - 1 = 2

cross product operations.

GATE CS 2024 Set 2 — Question 45

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Correct answer

Solution

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