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Each row above is really \(\{a_i\} \times B\) for some \(a_i \in A\text{.}\) That is, we fixed the \(A\)-element. Broken up this way, we have
\begin{equation*}
A \times B = (\{a_1\} \times B) \cup (\{a_2\} \times B) \cup (\{a_3\}\times B) \cup \cdots \cup (\{a_m\} \times B)\text{.}
\end{equation*}
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