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For $n\geq 1$, let $S_{n}$ denote the group of all permutations on $n$ symbols. Which of the following statements is true?

  1. $S_{3}$ has an element of order $4$
  2. $S_{4}$ has an element of order $6$
  3. $S_{4}$ has an element of order $5$
  4. $S_{5}$ has an element of order $6$.
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