1
GATE CSE 2006
+1
-0.3
Which of the following relational query languages have the same expressive power?

I) Relational algebra
II) Tuple relational calculus restricted to safe expressions
III) Domain relational calculus restricted to safe expressions

A
II and III only
B
I and II only
C
I and III only
D
I, II and III
2
GATE CSE 2005
+1
-0.3

Let r be a relation instance with schema R = (A, B, C, D).

We define $${r_1} = {\pi _{A,B,C}}\left( r \right)$$ and $${r_1} = {\pi _{A,D}}\left( r \right)$$. Let $$s = {r_1}*{r_2}$$ where * denotes natural join. Given that the decomposition of r into r1 and r2 is lossy, which one of the following is TRUE?
A
$$s \subset r$$
B
$$r \cup s =r$$
C
$$r \subset s$$
D
$$r * s = s$$
3
GATE CSE 2004
+1
-0.3
Let R1 (A, B, C) and R2 (D, E) be two relation schema, where the primary keys are shown underlined, and let C be a foreign key in R1 referring to R2. Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances r1 and r2. Which one of the following relational algebra expressions would necessarily produce an empty relation?
A
$$\prod\nolimits_D {\left( {{r_2}} \right)} - \prod\nolimits_C {\left( {{r_1}} \right)}$$
B
$$\prod\nolimits_C {\left( {{r_1}} \right)} - \prod\nolimits_D {\left( {{r_2}} \right)}$$
C
$$\prod\nolimits_D {\left( {{r_1}{ \Join _{C \ne D}}{r_2}} \right)}$$
D
$$\prod\nolimits_C {\left( {{r_1}{ \Join _{C = D}}{r_2}} \right)}$$
4
GATE CSE 2003
+1
-0.3
Consider the following SQL query:
Select distinct a1, a2, ..., an

From r1, r2, ..., rm

Where P; 
For an arbitrary predicate P, this query is equivalent to which of the following relational algebra expressions?
A
$$\prod\limits_{{a_1},{a_2},....,{a_n}} {{\sigma _p}} \left( {{r_1} \times {r_2} \times .... \times {r_m}} \right)$$
B
$$\prod\limits_{{a_1},{a_2},....,{a_n}} {{\sigma _p}} \left( {{r_1} \Join {r_2} \Join .... \Join {r_m}} \right)$$
C
$$\prod\limits_{{a_1},{a_2},....,{a_n}} {{\sigma _p}} \left( {{r_1} \cup {r_2} \cup .... \cup {r_m}} \right)$$
D
$$\prod\limits_{{a_1},{a_2},....,{a_n}} {{\sigma _p}} \left( {{r_1} \cap {r_2} \cap .... \cap {r_m}} \right)$$
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