Which of the following relational query languages have the same expressive power?

I) Relational algebra
II) Tuple relational calculus restricted to safe expressions
III) Domain relational calculus restricted to safe expressions

Consider the relations r₁(P, Q, R) and r₂(R, S, T) with primary keys P and R respectively. The relation r₁ contains 2000 tuples and r₂ contains 2500 tuples. The maximum size of the join $${r_1} \Join {r_2}$$ is

Consider a database with three relation instances shown below. The primary keys for the Drivers and Cars relation are Did and cid respectively and the records are stored in ascending order of these primary keys as given in the tables. No indexing is available in the database.

D: Drivers Relation

Did	Dname	rating	Age
22	Karthikeyan	7	25
29	Salman	1	33
31	Boris	8	55
32	Amoldt	8	25
58	Schumacher	10	35
64	Sachin	7	35
71	Senna	10	16
74	Sachin	9	35
85	Rahul	3	25
95	Ralph	3	53

R: Reserves Relation

Did	cid	Day
22	101	10/10/06
22	102	10/10/06
22	103	8/10/06
22	104	7/10/06
31	102	10/11/06
31	103	6/11/06
31	104	12/11/06
64	101	5/9/06
64	102	8/9/06
74	103	8/9/06

C: Cars relation

cid	Cname	Color
101	Renault	Blue
102	Renault	Red
103	Ferrari	Green
104	Jaguar	Red

What is the output of the following SQL query?

Select D.dname 
From Drivers D 
Where D.did in (SELECT R.did 
                From Cars C,Reserves R 
                WHERE R.cid = C.cid and C.color = 'green')

Consider a database with three relation instances shown below. The primary keys for the Drivers and Cars relation are Did and cid respectively and the records are stored in ascending order of these primary keys as given in the tables. No indexing is available in the database.

D: Drivers Relation

Did	Dname	rating	Age
22	Karthikeyan	7	25
29	Salman	1	33
31	Boris	8	55
32	Amoldt	8	25
58	Schumacher	10	35
64	Sachin	7	35
71	Senna	10	16
74	Sachin	9	35
85	Rahul	3	25
95	Ralph	3	53

R: Reserves Relation

Did	cid	Day
22	101	10/10/06
22	102	10/10/06
22	103	8/10/06
22	104	7/10/06
31	102	10/11/06
31	103	6/11/06
31	104	12/11/06
64	101	5/9/06
64	102	8/9/06
74	103	8/9/06

C: Cars relation

cid	Cname	Color
101	Renault	Blue
102	Renault	Red
103	Ferrari	Green
104	Jaguar	Red

Select D.dname 
From Drivers D 
Where D.did in (SELECT R.did 
                From Cars C,Reserves R 
                WHERE R.cid = C.cid and C.color = 'green')

Let n be the number of comparisons performed when the above SQL query is optimally executed. If linear search is used to locate a tuple in a relation using primary key, then n lies in the range