Consider the following relations A, B and C:
A

ID	Name	Age
12	Arun	60
15	Shreya	24
99	Rohit	11

B

ID	Name	Age
15	Shreya	24
25	Hari	40
98	Rohit	20
99	Rohit	11

C

ID	Phone	Area
10	2200	02
99	2100	01

How many tuples does the result of the following relational algebra expression contain? Assume that the schema of A ∪ B is the same as that of A. $$(A\cup B)\bowtie _{A.Id > 40 \vee C.Id < 15} C$$

Consider a relational table r with sufficient number of records, having attributes A₁, A₂,....., A_n and let 1 $$ \le $$ p $$ \le $$ n. Two queries Q1 and Q2 are given below.

$$Q1: \pi_{A_1, \dots ,A_p} \left(\sigma_{A_p=c}\left(r\right)\right)$$ where is a constant

$$Q2: \pi_{A_1, \dots ,A_p} \left(\sigma_{c_1 \leq A_p \leq c_2}\left(r\right)\right)$$ where c₁ and c₂ are constants

The database can be configured to do ordered indexing on A_p or hashing on A_p. Which of the following statements is TRUE?

The following functional dependencies hold for relations R(A, B, C) and S(B, D, E): $$$\eqalign{ & B \to A \cr & A \to C \cr} $$$

The relation R contains 200 tuples and the relation S contains 100 tuples. What is the maximum number of tuples possible in the natural join R $$\Join$$ S?

Let R and S be two relations with the following schema

R (P, Q, R1, R2, R3)

S (P, Q, S1, S2)

Where {P, Q} is the key for both schemas. Which of the following queries are equivalent?
I. $$\Pi_P \left(R \bowtie S\right)$$
II. $$\Pi_P \left(R\right) \bowtie \Pi_P\left(S\right)$$
III. $$\Pi_P \left(\Pi_{P, Q} \left(R\right) \cap \Pi_{P,Q} \left(S\right) \right)$$
IV. $$\Pi_P \left(\Pi_{P, Q} \left(R\right) - \left(\Pi_{P,Q} \left(R\right) - \Pi_{P,Q} \left(S\right)\right)\right)$$