# Give a two-sentence synopsis of Proof 2 of Theorem 9.15. Data from 9.15 Theorem No permutation in

## Question:

Give a two-sentence synopsis of Proof 2 of Theorem 9.15.

**Data from 9.15 Theorem**

No permutation in S_{n} can be expressed both as a product of an even number of transpositions and as a product of an odd number of transposition.

Proof 2 of 9.15 Theorem

Let a ∈ S_{n} and let r = (i, j) be a transposition in S_{n}. We claim that the number of orbits of σ and of r σ differ by 1.

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