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Size of the Power Set of A × B
publish date: 2026/05/23 22:20:51.101210 UTC
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If |A|=m and |B|=n, how many distinct relations from A to B are possible?
Correct Answer
\(2^{mn}\)
Explanation
A relation from \(A\) to \(B\) is any subset of \(A \times B\). The number of elements in \(A \times B\) is \(mn\). The number of subsets of a set with \(mn\) elements is \(2^{mn}\). Therefore, there are \(2^{mn}\) distinct relations. For example, if \(|A| = 2\) and \(|B| = 2\), then \(|A \times B| = 4\) and there are \(2^4 = 16\) possible relations.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012