If a relational decomposition is not dependency-preserving, which one of the following relational operators will be executed more frequently in order to maintain the dependencies?

Consider the following three relations:

Car (model, year, serial, color)

Make (maker, model)

Own (owner, serial)

A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. ( $\bowtie $ denotes natural join)

$$ \pi_{\text {owner }}(\text { Own } \bowtie \left(\sigma_{\text {color="red" }}\right. $$

$\left(\right.$ Car $\triangleright \triangleleft\left(\sigma_{\text {maker }=\text { "ABC }}\right.$ Make $\left.\left.\left.)\right)\right)\right)$

Which one of the following options describes what the above expression computes?

$$ \text { On a relation named Loan of a bank: } $$

The following SQL query is executed

SELECT L1.loan_number

FROM Loan L1

WHERE L1.amount > (SELECT MAX

(L2.amount)

FROM Loan L2

WHERE L2.branch_name $=$ 'SR Nagar');

The number of rows returned by the query is _________

Consider a fact table in an OLAP application: Facts (D1, D2, val), where D1 and D2 are its dimension attributes and val is a dependent attribute. Suppose

attribute D1 takes 3 values and D2 takes 2 values, and all combinations of these values are present in the table Facts. How many tuples are there in the result of the following query?

SELECT D1, D2, sum(val)

FROM Facts

GROUP BY CUBE (D1, D2);