The keys 12, 18, 13, 2, 3, 23, 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h(k) = k mod 10 and linear probing. What is the resultant hash table?

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?

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?