Over a relation Borrow$($reader$,$book,date$),$ consider the following SQL expression:

with B as

$($select book, count$(*)$ as number

from Borrow

group by book$)$

select $*$

from B natural join

$($select max$($number$)$ as number from B$)$

Which statements are correct? $($In relational algebra we use project to indicate projections and sigma to indicate selections.$)$

The same query can be equivalently written in SQL as follows:

with Maxbook as

$($select book, max$($date$)$ as number

from Borrow

group by book, reader$)$

select book, number

from Borrow natural join Maxbook

The following SQL expression is NOT equivalent:

select book, max$($number$)$

from $($select book, count$(*)$ as number

from Borrow

group by book$)$

group by book

This expression returns, for each book, the maximum number of readers who borrowed it$.$

This expression returns the book $($or books$)$ that has been borrowed by the largest number of different readers.

This expression returns the book $($or books$)$ that has been borrowed the most often, together with the number of times it was borrowed.