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Number of Elements in A × B
publish date: 2026/05/23 22:20:48.103292 UTC
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If set \(A\) contains \(m\) elements and set \(B\) contains \(n\) elements, how many ordered pairs are in the Cartesian product \(A \times B\)?
Correct Answer
\(m \times n\)
Explanation
The Cartesian product \(A \times B\) is the set of all ordered pairs \((a, b)\) where \(a \in A\) and \(b \in B\). There are \(m\) choices for the first element and \(n\) choices for the second, resulting in \(m \cdot n\) ordered pairs. For example, if \(A = \{1, 2\}\) and \(B = \{3, 4, 5\}\), then \(|A \times B| = 2 \times 3 = 6\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012