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Question.

  1. Let f be the element of S, which has been written in two-line notation. Write f in cycle notation.
  2. Let g be the element of S, which has been written in cycle notation. Write g in two-line notation.
  3. Compute the inverse of f. Try doing the computation in each of our two notations.
  4. Compute the composition f ○ g. Try doing the computation in each of our two notations.

Answer.

  1. f = .
  2. g = .
  3. f-1 = = .
  4. f ○ g = = .
Bear in mind that cycle notation is not unique: your answer could still be correct if your cycles came in different order or started at different places, or you included cycles of length 1.