For each of the following queries, identify one possible reason why an optimizer might not find a good plan. Rewrite the query so that a good plan is likely to be found. Any available indexes or known constraints are listed before each query; assume that the relation schemas are consistent with the attributes referred to in the query.

1. An index is available on the age attribute:

SELECT E.dno

FROM Employee E

WHERE E.age=20 OR E.age=10

2. A B+ tree index is available on the age attribute:

SELECT E.dno

FROM Employee E

WHERE E.age<20 AND E.age>10

3. An index is available on the age attribute:

SELECT E.dno

FROM Employee E

WHERE 2*E.age<20

4. No index is available:

SELECT DISTINCT *

FROM Employee E

5. No index is available:

SELECT AVG (E.sal)

FROM Employee E

GROUP BY E.dno

HAVING E.dno=22

6. The sid in Reserves is a foreign key that refers to Sailors:

SELECT S.sid

FROM Sailors S, Reserves R

WHERE S.sid=R.sid