Question: Functions For these problems, let Sv be the set of numbers 1,2,3,…, N]) 1) How many functions a…
Just answer number 5 only please.
![Functions For these problems, let Sv be the set of numbers 1,2,3,..., N]) 1) How many functions are there that map SN to SN 2) Argue that if a map f : SN SN is surjective, then f is a bijection. 3) Argue that if a map f SNSv is injective, then f is a bijection 4) How many bijections are there that map Sv to Sv? 5) Suppose f is a map from a set S to itself, f : s → s. * If S is a finite set, argue that If(S)- S if and only if f is a bijection * Give an example of an infinite S and an f such that is not a bijection, but If (S)S . f is a bijection, but f (S) is a proper subset of S.](https://media.cheggcdn.com/media%2F960%2F9602747c-8245-45f2-80a7-e3e7cdb51240%2Fimage.png)
Show transcribed image text Functions For these problems, let Sv be the set of numbers 1,2,3,…, N]) 1) How many functions are there that map SN to SN 2) Argue that if a map f : SN SN is surjective, then f is a bijection. 3) Argue that if a map f SNSv is injective, then f is a bijection 4) How many bijections are there that map Sv to Sv? 5) Suppose f is a map from a set S to itself, f : s → s. * If S is a finite set, argue that If(S)- S if and only if f is a bijection * Give an example of an infinite S and an f such that is not a bijection, but If (S)S . f is a bijection, but f (S) is a proper subset of S.
Functions For these problems, let Sv be the set of numbers 1,2,3,…, N]) 1) How many functions are there that map SN to SN 2) Argue that if a map f : SN SN is surjective, then f is a bijection. 3) Argue that if a map f SNSv is injective, then f is a bijection 4) How many bijections are there that map Sv to Sv? 5) Suppose f is a map from a set S to itself, f : s → s. * If S is a finite set, argue that If(S)- S if and only if f is a bijection * Give an example of an infinite S and an f such that is not a bijection, but If (S)S . f is a bijection, but f (S) is a proper subset of S.
