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Define the sign of a permutation $ to be:

sgn $ = 1 if $ is even. -1 if $ is odd.

Prove that sgn($%) = sgn$sgn% for all $ and % in Sn.

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Solution Summary

A proof involving the signs of permutations is provided. The proof is concise.

Solution Preview

We know each permutation can be expressed as the products of 2-cycles. 2-cycle is the form of (ab). If a permutation has odd ...

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