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Problem threeLet A and B be the sets of even an odd permutations of Sn respectively: Define0 : A+B such thato(p) 0(12).Is injective?(b) Is surjective?Does define an...

Question

Problem threeLet A and B be the sets of even an odd permutations of Sn respectively: Define0 : A+B such thato(p) 0(12).Is injective?(b) Is surjective?Does define an isomorphism?

Problem three Let A and B be the sets of even an odd permutations of Sn respectively: Define 0 : A+B such that o(p) 0(12). Is injective? (b) Is surjective? Does define an isomorphism?



Answers

If $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is a bijection, then (a) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{B})$ (b) $\mathrm{n}(\mathrm{A})>\mathrm{n}(\mathrm{B})$ (c) $\mathrm{n}(\mathrm{A})<\mathrm{n}(\mathrm{B})$ (d) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{b})+1$


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