In a schema with attributes $$A, B, C, D,$$ and $$E,$$ following set of functional dependencies are given
$$\eqalign{ & \,\,\,A \to B \cr & \,\,\,A \to C \cr & CD \to E \cr & \,\,\,B \to D \cr & \,\,\,E \to A \cr} $$

Which of the following functional dependencies is NOT implied by the above set?

Consider a relation scheme $$R = \left( {A,\,B,\,C,\,D,\,E,\,H} \right)$$ on which the following functional dependencies hold: $$\left\{ {A \to B,\,\,BC \to D,\,\,E \to C,\,\,D \to A} \right\}.$$ What are the candidate keys of $$R?$$

The relation book (title, price) contains the titles and prices of different books. Assuming that no two books have the same price, what does the following SQL query list?

Select title
 From book as B
 Where (select count(*)
   From book as T
   Where T.price > B.price) < 5;

A company maintains records of sales made by its salespersons and pays them commission based on each individual’s total sales made in a year. This data is maintained in a table with following schema:

salesinfo = (salespersonid, totalsales, commission)

In a certain year, due to better business results, the company decides to further reward its salespersons by enhancing the commission paid to them as per the following formula:

If commission < = 50000, enhance it by 2%
If 50000 < commission < = 100000, enhance it by 4%
If commission > 100000, enhance it by 6%

The IT staff has written three different SQL scripts to calculate enhancement for each slab, each of these scripts is to run as a separate transaction as follows:

T1: Update salesinfo
 Set commission = commission * 1.02
 Where commission < = 50000;

T2: Update salesinfo
 Set commission = commission * 1.04
 Where commission > 50000 and commission is < = 100000;

T3: Update salesinfo
 Set commission = commission * 1.06
 Where commission > 100000;

Which of the following options of running these transactions will update the commission of all salespersons correctly?