Prove that if (S) is a set and (S_{1}, ldots, S_{k}) is a partition of (S), then
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Prove that if \(S\) is a set and \(S_{1}, \ldots, S_{k}\) is a partition of \(S\), then there is a unique equivalence relation \(\sim\) on \(S\) that has the \(S_{i}\) as its equivalence classes.
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