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 a join (relation algebra) between relations r(R)and s(S) using the nested loop method. There are 3 buffers each of size equal to disk block size, out of which one buffer is reserved for intermediate results. Assuming size(r(R)) < size(s(S)), the join will have fewer number of disk block accesses if