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

To find cities with at least 3 persons, we need to compare three distinct person records residing in the same city.

1. Let $P_1, P_2, P_3$ be three renamed instances of the relation Person:

   $$P_1 = \rho(P_1, \text{Person}), \quad P_2 = \rho(P_2, \text{Person}), \quad P_3 = \rho(P_3, \text{Person})$$

2. To bring the three tuples together into a single relation, we perform cross products:

   $$(P_1 \times P_2) \times P_3$$

   Combining 3 instances of a relation requires 2 cross product operations.

3. We then apply selection to ensure that all three tuples have the same city but distinct pids:

   $$\sigma_{P_1.city = P_2.city \,\land\, P_2.city = P_3.city \,\land\, P_1.pid \neq P_2.pid \,\land\, P_2.pid \neq P_3.pid \,\land\, P_1.pid \neq P_3.pid}\big((P_1 \times P_2) \times P_3\big)$$

4. Finally, project on the city name:

   $$\Pi_{P_1.city}(\dots)$$

Therefore, the minimum number of cross product operations required is 2 (Option B).