Amongst the ACID properties of a transaction, the 'Durability' property requires that the changes made to the database by a successful transaction persist

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 table ‘student’ with schema (roll, name, hostel, marks), and another table ‘hobby’ with schema (roll, hobbyname) contains records as shown below:

Table: student

Roll	Name	Hostel	Marks
1798	Manoj Rathod	7	95
2154	Soumic Banerjee	5	68
2369	Gumma Reddy	7	86
2581	Pradeep Pendse	6	92
2643	Suhas Kulkarni	5	78
2711	Nitin Kadam	8	72
2872	Kiran Vora	5	92
2926	Manoj Kunkalikar	5	94
2959	Hemant Karkhanis	7	88
3125	Rajesh Doshi	5	82

Table: hobby

Roll	Hobbyname
1798	chess
1798	music
2154	music
2369	swimming
2581	cricket
2643	chess
2643	hockey
2711	volleyball
2872	football
2926	cricket
2959	photography
3125	music
3125	chess

The following SQL query is executed on the above tables:

Select hostel
From student natural join hobby
Where marks > = 75 and roll between 2000 and 3000;

Relations S and H with the same schema as those of these two tables respectively contain the same information as tuples. A new relation S’ is obtained by the following relational algebra operation:

$$\eqalign{ & S' = \prod\nolimits_{hostel} {(({\sigma _{S.roll = H.roll}}} \cr & ({\sigma _{marks > 75\,\,\,and\,\,roll > 2000\,\,and\,\,roll < 3000}}(S))X(H)) \cr} $$

The difference between the number of rows output by the SQL statement and the number of tuples in S’ is

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?