Let \(k\) be a positive integer with \(k \leq |S_n|\). The symmetric group \(S_n\) acts on the set B consisting of all k-element subsets of \({1, \ldots , n}\) by \(\sigma \cdot {a_1, \ldots, a_k}={\sigma(a_1),\ldots,\sigma(a_k)}\).
Determine for which values of \(k\) the actions of \(S_n\) on k-element subsets is faithul

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Egh, I can't type: \(\{\sigma(a_1), \ldots , \sigma(a_k)\}\)

\(S_n\) is a group and it's operation is symmetric?

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