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[03C] Let \(C\) be a set, \(I\) a family of indices, and \(B\) sets for \(i\in I\) with \(| B_ i|=| C|\); then show that
\[ \left|{\mathcal B}\right| = \left|C^ I\right| \]
where \({\mathcal B}=\prod _{i\in I} B_ i\).
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