Question

Given two relations R1(A, B) and R2(C, D), the result of following query

Select distinct A, B from R1, R2 is guaranteed to be same as R1 provided one of the following condition is satisfied.
o R1 has no duplicates and R2 is empty.
o R1 has no duplicates and R2 is non-empty.
o Both R1 and R2 have no duplicates.
o R2 has no duplicates and R1 is non - empty

Answer 1

The conditions under which the SQL query 'Select distinct A, B from R1, R2' produces an output identical to R1 relate to the absence of duplicates in R1 and R2, and whether R2 is empty or not.

Step-by-step explanation:

The question pertains to the concept of database relations and SQL queries, specifically the Cartesian product of two relations and the conditions under which the result of a query would be identical to one of the original relations.

To ensure that the query Select distinct A, B from R1, R2 will result in the same set as R1, one of the following conditions should be satisfied: either R1 contains no duplicates and R2 is empty, or R1 contains no duplicates and R2 is non-empty (assuming R2 does not affect the content of A and B from R1), or both R1 and R2 have no duplicates but are unrelated so that the combination does not create duplicates in A and B from R1. If R2 has no duplicates and R1 is non-empty, it does not guarantee the same output as R1 because R2 could still have an effect on the results.

In terms of probability, mutually exclusive events are those which cannot occur simultaneously, such as sets A and C where P(A AND C) = 0. If it's not known whether two events are mutually exclusive, we should not assume they are until proven otherwise. Furthermore, the independence of events means that the occurrence of one event does not affect the occurrence of another, which can be checked if P(A AND B) does not equal P(A)P(B).