Question

Consider two tables R and S with cardinalities \(m\) and \(n\) respectively. What is the maximum cardinality of the result of relational algebraic operation \(R \cup S\)?

• A. \(m\times n\)
• B. \(m+n\)
• C. \(\max(m,n)\)
• D. \(m\)

Hint:

For Union: \[ \max(|R\cup S|)=|R|+|S| \] when there are no common tuples.

Answer 1

The Correct Option is B

Concept: Union combines tuples from two union-compatible relations. Duplicate tuples are removed.

Step 1: Understand Union operation.
For relations \[ R \] and \[ S \] \[ R \cup S \] contains all tuples present in either relation.

Step 2: Determine maximum cardinality.
The maximum number of tuples occurs when the two relations have no common tuples. In that case, \[ |R \cup S| = |R|+|S| \] \[ = m+n \]

Step 3: Select the answer.
Therefore, \[ \boxed{m+n} \] is the maximum cardinality.