Question

Which of the following operation combines tuples from two relations resulting in all pairs of rows from the two input relations, regardless of whether or not they have the same values on common attributes?

• A. Union
• B. Cartesian Product
• C. Join
• D. Intersection

Hint:

For Cartesian Product ($R \times S$):
- Cardinality (Number of rows) = $\text{Cardinality}(R) \times \text{Cardinality}(S)$.
- Degree (Number of columns) = $\text{Degree}(R) + \text{Degree}(S)$.
This is a standard calculation tested in exams.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to identify the relational algebra operation that pairs every row of one relation with every row of another, without checking for any match on common attribute values.

Step 2: Key Formula or Approach:
Let us review the fundamental database operations:
- Union: Combines rows from two relations that are union-compatible (same schema).
- Cartesian Product (denoted as $R \times S$): Generates all possible ordered pairs of tuples from relation $R$ and $S$.
- Join: Combines matching rows based on a specific predicate.
- Intersection: Yields only the rows that exist in both relations.

Step 3: Detailed Explanation:
The Cartesian Product operation does not look at the actual values of attributes.
If relation $R$ has $m$ rows and relation $S$ has $n$ rows, the Cartesian Product will always yield $m \times n$ rows.
Each tuple of $R$ is paired with every tuple of $S$ sequentially.
Joins, such as Equi-Join or Natural Join, only combine those tuples that share matching values on their common attributes.
Therefore, the operation that creates all possible pairs of rows regardless of common attributes is the Cartesian Product.
Thus, Option (B) is correct.

Step 4: Final Answer:
The correct option is (B).