= (a) Provide a proof for the fact that the sign function on Sn is multiplicative, meaning sign(TTO) = sign() sign(o) 7

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A Provide A Proof For The Fact That The Sign Function On Sn Is Multiplicative Meaning Sign Tto Sign Sign O 7 1 (69.44 KiB) Viewed 23 times

= (a) Provide a proof for the fact that the sign function on Sn is multiplicative, meaning sign(TTO) = sign() sign(o) 7 for all 1,0 E Sn. (b) Prove that the set An := {T E Sn | sign(7) 1} has mi elements for all n > 2. Show this by constructing a suitable bijective mapping between An and Sn \ An. Remark: Without justification, you may use the fact that if there is a bijective mapping between two (finite) sets, then these must have the same number of elements. : = 2