To retrieve the names of players who play for the team with tname = \text{'MI^{\prime}} using Tuple Relational Calculus (TRC):
The target tuple variable p must represent a tuple from the relation players, since we are selecting player names (p.pname) from players (p∈players).
We need to check the condition on the corresponding team, which requires an existential quantifier ∃t over the teams relation (t∈teams).
The join condition between the player and their team is p.tid=t.tid.
The team selection condition is t.tname = \text{'MI^{\prime}}.
Combining these conditions gives:
\{ p.pname \mid p \in players \wedge \exists t\, (t \in teams \wedge p.tid = t.tid \wedge t.tname = \text{'MI^{\prime}}) \}
Option (A) correctly defines p∈players, joins with t∈teams via p.tid=t.tid, and checks t.tname = \text{'MI^{\prime}}.
Option (B) incorrectly specifies p∈teams while selecting p.pname, but pname is not an attribute of teams.
Option (C) lacks the join condition p.tid=t.tid.
Option (D) incorrectly specifies p∈teams and lacks the join condition.