Consider two relations describing \(𝑡𝑒𝑎𝑚𝑠 \) and \(𝑝𝑙𝑎𝑦𝑒𝑟𝑠 \) in a…

Correct expression: { p.pname | p ∈ players ∧ ∃t (t ∈ teams ∧ p.tid = t.tid ∧ t.tname = 'MI') }

Why this is correct:

• The main variable p ranges over the players relation, so p.pname refers to a valid player name.

• The existentially quantified tuple t ranges over teams and provides the team context to test.

• The equality p.tid = t.tid links a player to their team, ensuring we only consider the player's own team.

• The condition t.tname = 'MI' filters to the specific team named 'MI'. Combined, these return exactly the players who play for 'MI'.

Why the other expressions are wrong:

• Expressions that bind the main variable to the teams relation and then try to return p.pname are invalid because team tuples do not have a player-name attribute.

• Expressions that omit the equality p.tid = t.tid fail to link players to teams; such a query would return every player's name whenever any team named 'MI' exists, which is not the intended result.

• Swapping the roles of the quantified relation (making the existential range over players while treating the main variable as a team) also mismatches attributes and produces incorrect or meaningless conditions.

Summary: The correct query binds the result variable to players, uses an existential team tuple to find a matching team by id, and filters that team by name 'MI'.