Consider a relational database schema with two relations $R(P, Q)$ and $S(X, Y)$.

Let $E=\{\langle u\rangle \mid \exists v \exists w\langle u, v\rangle \in R \wedge\langle v, w\rangle \in S\}$ be a tuple relational calculus expression. Which one of the following relational algebraic expressions is equivalent to $E$ ?

Consider two relations describing teams and players in a sports league:

$\bullet$ teams(tid, tname): tid, tname are team-id and team-name, respectively.

$\bullet$ players(pid, pname, tid): pid, pname, and 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 tname as ' $M I$ '?

The relation schema, Person($\underline{\text{pid}}$, $city$), 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