Consider the following relational schema:

Suppliers(sid : integer, sname : string, city : string, street : string)

Parts(pid : integer, pname : string, color : string)

Catalog(sid : integer, pid : integer, cost : real)

Consider the following relational query on the above database:

SELECT S.sname 
FROM Suppliers S 
WHERE S.sid NOT IN 
     (SELECT C.sid 
      FROM Catalog C 
      WHERE C.pid NOT IN 
        (SELECT P.pid 
         FROM Parts P 
         WHERE P.color<> 'blue'))

Assume that relations corresponding to the above schema are not empty. Which one of the following is the correct interpretation of the above query?

Consider the following relational schema:

Suppliers(sid : integer, sname : string, city : string, street : string)

Parts(pid : integer, pname : string, color : string)

Catalog(sid : integer, pid : integer, cost : real)

Assume that, in the suppliers relation above, each supplier and each street within a city has a unique name, and (sname, city) forms a candidate key. No other functional dependencies are implied other than those implied by primary and candidate keys. Which one of the following is TRUE about the above schema?

Consider two transactions T₁ and T₂ and four schedules S₁, S₂, S₃, S₄ of T₁ and T₂ as given below:

T₁: R₁[ x ] W₁[ x ] W₁[ y ]
T₂: R₂[ x ] R₂[ y ] W₂[ y ]
S₁: R₁[ x ] R₂[ x ] R₂[ y ] W₁[ x ] W₁[ y ] W₂[ y ]
S₂: R₁[ x ] R₂[ x ] R₂[ y ] W₁[ x ] W₂[ y ] W₁[ y ]
S₃: R₁[ x ] W₁[ x ] R₂[ x ] W₁[ y ] R₂[ y ] W₂[ y ]
S₄: R₂[ x ] R₂[ y ] R₁[ x ] W₁[ x ] W₁[ y ] W₂[ y ]

Which of the above schedules are conflict-serializable?

Let R and S be relational schemes such that R = { a, b, c } and S = { c }. Now consider the following queries on the database:

I. $$\pi_{R-S}(r) - \pi_{R-S} \left (\pi_{R-S} (r) \times s - \pi_{R-S,S}(r)\right )$$

II. $$\left\{t \mid t \in \pi_{R-S} (r) \wedge \forall u \in s \left(\exists v \in r \left(u = v[S] \wedge t = v\left[R-S\right]\right )\right )\right\}$$

III.$$\left\{t \mid t \in \pi_{R-S} (r) \wedge \forall v \in r \left(\exists u \in s \left(u = v[S] \wedge t = v\left[R-S\right]\right )\right ) \right\}$$

IV. Select R.a, R.b
    From R, S
    Where R.c = S.c

Which of the above queries are equivalent?