Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).

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

Consider the relations $$r(A, B)$$ and $$s(B, C),$$ where $$s.B$$ is a primary key and $$r.B$$ is a foreign key referencing $$s.B.$$ Consider the 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 $$Q$$?

Consider two relations $${R_1}\left( {A,B} \right)$$ with the tuples $$(1,5), (3,7)$$ and $${R_2}\left( {A,C} \right) = \left( {1,7} \right),\left( {4,9} \right).$$
Assume that $$R(A,B,C)$$ is the full natural outer join of $${R_1}$$ and $${R_2}$$. Consider the following tuples of the form $$(A,B,C): a = (1,5,null),$$ $$b = (1,null,7),$$ $$c = (3, null, 9),$$ $$d = (4,7,null),$$ $$e = (1,5,7),$$ $$f = (3,7,null),$$ $$g = (4,null,9).$$ Which one of the following statements is correct?

Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation:

employee (empId, empName, empAge)

dependent (depId, eId, depName, depAge)

Consider the following relational algebra query: $$\Pi_{empId}\:(employee) - \Pi_{empId}\:(employee \bowtie_{(empId=eID) \wedge (empAge \leq depAge)} dependent)$$

The above query evaluates to the set of empIds of employees whose age is greater than that of