Each row of the following table shows two queries. In the blank third column of

Question

Each row of the following table shows two queries. In the blank third column of the table write "YES" if the two queries are equivalent, and "NO" if they are not equivalent. 5. All queries refer to a schema containing two relations: R(A, B) where A is a key and B is a key. S(A, B) where A is a key. You may assume the relations do not contain NULL values. Query 1 TA(R - S) TB(R- S) Query 2 TA(R) TA(S) TBR) TB(S) quiv.? select R . A from R,S where R.B=$.B select R.B from R,S where R. A-s. A select min(B) from R TB(R) select max (B) from R

Explanation / Answer

1. NO

if R={(1,2),(1,3)} and S={(1,1),(1,2)} then

query1= {(1)} while query2 = {}

2. NO

if R={(1,2),(1,3)} and S={(1,1),(1,2)} then

query1= {(1)} while query2 = {(2)}

3. YES

As all the tuples will be included. Hence, both queries are equivalent.
if R={(1,2),(2,3)} and S={(1,1),(1,2)} then
query1= {(1),(2),(3)} while query2 = {(1),(2),(3)}

4. NO

Since, the result of join operation will have only those tuples for which the value of R.A and S.A are same. Hence, the two queries are not equivalent.
if R={(5,2),(2,3)} and S={(1,1),(2,2)} then
query1= {(5,2)} while query2 = { }

5. YES.

Query2 is the SQL statement for query1.

6. YES

Query2 is the SQL statement for query1.

7. YES

Since, the selection on the cross product will select those tuples whose R1.B is atleast greater than one of the element. The projection will select all the elements except the minimum. Hence, the result is min(R.B)

8. YES

Since, the selection on the cross product will select those tuples whose R1.B is atleast smallerr than one of the element. The projection will select all the elements except the maximum. Hence, the result is max(R.B)

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