GATE CS 2025 Set 1 Q.39: Relational Algebra and Tuple Relational Calculus

Consider two relations describing $\textit{teams}$ and $\textit{players}$ in a sports league:

$\textit{teams}(\textit{tid}, \textit{tname})$ : $\textit{tid}, \textit{tname}$ are team-id and team-name, respectively
$\textit{players}(\textit{pid}, \textit{pname}, \textit{tid})$ : $\textit{pid}, \textit{pname},$ and $\textit{tid}$ denote player-id, player-name and the team-id of the player, respectively

Which ONE of the following tuple relational calculus queries returns the name of the players who play for the team having $\textit{tname}$ as $'MI'$ ?

$\{ p.\textit{pname} \mid p \in \textit{players} \wedge \exists t (t \in \textit{teams} \wedge p.\textit{tid} = t.\textit{tid} \wedge t.\textit{tname} = 'MI')\}$

$\{ p.\textit{pname} \mid p \in \textit{teams} \wedge \exists t (t \in \textit{players} \wedge p.\textit{tid} = t.\textit{tid} \wedge t.\textit{tname} = 'MI')\}$

$\{ p.\textit{pname} \mid p \in \textit{players} \wedge \exists t (t \in \textit{teams} \wedge t.\textit{tname} = 'MI')\}$

$\{ p.\textit{pname} \mid p \in \textit{teams} \wedge \exists t (t \in \textit{players} \wedge t.\textit{tname} = 'MI')\}$

Official answer and solution

Official answer: A
From: Official GATE 2025 answer key

Solution

Bind tuple variable $p$ to players, existentially quantify $t$ in teams, and join on $p.\textit{tid} = t.\textit{tid}$ with $t.\textit{tname} = 'MI'$ .

To retrieve p.pname, tuple variable $p$ must belong to the players relation ( $p \in \textit{players}$ ), and there must exist a tuple $t \in \textit{teams}$ that matches $p$ 's team ID ( $p.\textit{tid} = t.\textit{tid}$ ) and has team name 'MI' ( $t.\textit{tname} = 'MI'$ ). Option (A) states this exact query; (B) and (D) bind $p$ to teams, while (C) omits the join condition $p.\textit{tid} = t.\textit{tid}$ .

Final answer

Option (A)

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

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question: 39 of 65
Section: Computer Science and Information Technology

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