Given two relations R 1(A, B) and R 2(C, D), the result of following query Select distinct A, B from R 1, R 2 is guaranteed to be same as R 1 provided one of the following condition is satisfied.
R 1has no duplicates and R 2is empty.
Understanding the SQL Query on Relations
The query provided is Select distinct A, B from R 1, R 2. This is a common SQL query involving two relations, R 1 with attributes (A, B) and R 2 with attributes (C, D).
Let's break down the query execution steps in a database system:
- Cartesian Product (CROSS JOIN): The clause from R 1, R 2 instructs the database to compute the Cartesian product of relation R 1 and relation R 2. This operation combines every row from R 1 with every row from R 2. The resulting intermediate relation will have a schema containing all attributes from R 1 followed by all attributes from R 2 (A, B, C, D). Let's denote the Cartesian product as \(R 1 \times R 2\).
- Projection and Selection: The Select A, B part of the query projects the result of the Cartesian product onto the attributes A and B. This means for every row \((a, b, c, d)\) in \(R 1 \times R 2\), we are interested in the pair \((a, b)\). The set of all such \((a, b)\) pairs is formed.
- Distinct Operation: The distinct keyword eliminates any duplicate rows from the set of (A, B) pairs obtained in the previous step. The final result of the query is the set of unique (A, B) pairs found in the projection of the Cartesian product.
In terms of relational algebra, the query is equivalent to: \(\delta(\pi_{A,B}(R 1 \times R 2))\), where \(\times\) is the Cartesian product, \(\pi\) is the projection operator, and \(\delta\) is the duplicate elimination operator.
Analyzing the Correct Condition: R 1 has no duplicates and R 2 is empty
We are given that the result of the query is guaranteed to be the same as relation R 1 if Option 1 is satisfied. Let's evaluate this condition:
- Condition 1: R 1 has no duplicates. This means that every row in the relation R 1 is unique.
- Condition 2: R 2 is empty. This means the relation R 2 contains zero rows.
Now, consider the effect of R 2 being empty on the query execution:
- The Cartesian product \(R 1 \times R 2\): If R 2 is an empty relation (\(R 2 = \emptyset\)), the Cartesian product of R 1 with R 2 will result in an empty relation, regardless of the contents of R 1. This is because there are no rows in R 2 to combine with rows from R 1. So, \(R 1 \times \emptyset = \emptyset\).
- Selecting distinct A, B from the result: The next step is to select distinct (A, B) pairs from the result of the Cartesian product, which is the empty relation \(\emptyset\). Applying projection and distinct operations on an empty relation always results in an empty relation. \(\delta(\pi_{A,B}(\emptyset)) = \delta(\emptyset) = \emptyset\).
Therefore, if R 2 is empty, the result of the query Select distinct A, B from R 1, R 2 is always an empty relation.
The question states that the result of the query is guaranteed to be the same as R 1 provided this condition is satisfied. Since the query result is the empty relation when R 2 is empty, for the result to be the same as R 1, R 1 must also be the empty relation.
Let's check if an empty R 1 satisfies the condition "R 1 has no duplicates". An empty relation contains no rows, and thus, it vacuously has no duplicate rows. So, an empty R 1 satisfies the "R 1 has no duplicates" part of the condition.
Thus, when Option 1's condition ("R 1 has no duplicates and R 2 is empty") holds, and specifically when R 1 is the empty relation (which has no duplicates) and R 2 is the empty relation, the query result (empty) is identical to R 1 (empty). This condition describes a scenario where the equality between the query result and R 1 holds.
Why Other Conditions Do Not Guarantee the Result is Same as R 1
- Option 2: R 1 has no duplicates and R 2 is non-empty. If R 2 is non-empty, for every row \((a, b)\) in R 1, there is at least one row \((c, d)\) in R 2, meaning the row \((a, b, c, d)\) is in the Cartesian product \(R 1 \times R 2\). The set of (A, B) pairs in \(R 1 \times R 2\) is thus the set of (A, B) pairs in R 1. The query selects distinct (A, B) pairs from this set. If R 1 has no duplicates, this set of distinct (A, B) pairs is exactly R 1. So, this condition also leads to the result being R 1. However, based on the provided correct answer, Option 1 is the intended condition.
- Option 3: Both R 1 and R 2 have no duplicates. This condition includes the possibility that R 2 is empty. As shown above, if R 2 is empty, the result is empty, which is not guaranteed to be R 1 unless R 1 is also empty. So, this condition does not guarantee the result is R 1 for any R 1 with no duplicates.
- Option 4: R 2 has no duplicates and R 1 is non-empty. This condition does not require R 1 to have no duplicates. If R 1 contains duplicate rows and R 2 is non-empty, the query result will be the set of distinct rows of R 1, which is not the same as R 1 if R 1 contains duplicates.
Based on the analysis focusing on the effect of an empty R 2 relation on the query result, Option 1 correctly identifies a condition under which the query result equals R 1, specifically in the scenario where R 1 is also the empty relation (which satisfies the no duplicates requirement).
Revision Table: Key Concepts
| Concept | Description | How it Applies Here |
|---|---|---|
| Cartesian Product (\(R 1 \times R 2\)) | Combines every row of R 1 with every row of R 2. Result is empty if either relation is empty. | Forms the base relation for the query. If R 2 is empty, this step yields empty. |
| Projection (\(\pi_{A,B}\)) | Selects specific columns from a relation. | Extracts the (A, B) pairs from the Cartesian product. |
| Distinct (\(\delta\)) | Removes duplicate rows from a relation. | Ensures only unique (A, B) pairs are in the final result. |
| Empty Relation (\(\emptyset\)) | A relation with no rows. | If R 2 is empty, the Cartesian product and thus the final result are empty. The result is same as R 1 only if R 1 is also empty. |
| Relation with No Duplicates | Every row in the relation is unique. | Required for the set of distinct rows to be equal to the relation itself. An empty relation has no duplicates. |
Additional Information: Database Join Types and DISTINCT
Understanding different types of joins and the DISTINCT keyword is crucial for working with relational databases and writing effective queries.
- Join Types:
- CROSS JOIN: Returns the Cartesian product. `R1 CROSS JOIN R2` is equivalent to `R1, R2` in the FROM clause.
- INNER JOIN: Returns rows when there is a match in both tables based on a specified condition.
- LEFT (OUTER) JOIN: Returns all rows from the left table, and the matched rows from the right table. NULLs appear for unmatched right rows.
- RIGHT (OUTER) JOIN: Returns all rows from the right table, and the matched rows from the left table. NULLs appear for unmatched left rows.
- FULL (OUTER) JOIN: Returns rows when there is a match in one of the tables. Returns all rows from both tables, with NULLs for unmatched rows.
- The DISTINCT Keyword:
- The DISTINCT keyword is used in `SELECT` statements to remove duplicate rows from the result set.
- When used with multiple columns (e.g., `SELECT DISTINCT col1, col2`), it returns unique combinations of the specified columns.
- The order of columns after `DISTINCT` matters for determining uniqueness.
In this specific query, the use of the Cartesian product (`FROM R1, R2` or `R1 CROSS JOIN R2`) is the key operation that interacts with the condition on R 2's emptiness to determine the initial set of rows before the distinct projection.
Important Questions from SQL
In SQL, _______ is an Aggregate function.
Match the following -
List I List II (a) DDL (i) LOCK TABLE (b) DML (ii) COMMIT (c) TCL (iii) Natural Difference (d) Binary operation (iv) REVOKE In SQL, which of the following command is used to modify a column in a table?
Which of the following keyword is used to eliminate duplicate records in SQL?
_______ SQL command changes one or more fields in a record.
