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

A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of σ_{(A>10)∨(B=18)}(r) is ______

How many tuples will be returned by the following relational algebra query?

$$Q:$$ $$\,\,\,\,\,\,\,\,\,$$ $$r$$ $$\,\,\,\,$$ $$\bowtie$$ $$\,\,\,\,$$ $$\left( {{\sigma _{b < 5}}\left( s \right)} \right)$$

Let $$LOJ$$ denote the natural left outer-join operation. Assume that $$r$$ and $$s$$ contain no null values.

Which one of the following queries is NOT equivalent to $$Q$$?