# Sets and Maps, I need some advice on the properties of these maps?

I have a few questions that I need help on, for two of them I believe I have a way to do them and in some cases an answer, however I am not certain that they are accurate.
1) For the map of phi: the set of natural numbers (starting with 0) goes to the set of integers with x mapped to x^6 (x--->x^6) Determine...
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I have a few questions that I need help on, for two of them I believe I have a way to do them and in some cases an answer, however I am not certain that they are accurate.

1) For the map of phi: the set of natural numbers (starting with 0) goes to the set of integers with x mapped to x^6 (x--->x^6) Determine whether the map is bijective.

I was thinking that this map would be injective but not surjective therefore making it not bijective. Is this correct?

2) This problem I need some help starting it: Let M and N be sets with k and l elements, respectively. Determine the number of possible maps from M to N.

3) Find and example of the maps phi:M-->N and psi: N-->P such that Psi of Phi is surjective but phi is not surjective. For this problem I was thinking that I would need to find a map where phi is not surjective and a map where psi is bijective in order to get psi of phi to be bijective and phi not to be surjective. Any thoughts?

Thanks.

1) For the map of phi: the set of natural numbers (starting with 0) goes to the set of integers with x mapped to x^6 (x--->x^6) Determine whether the map is bijective.

I was thinking that this map would be injective but not surjective therefore making it not bijective. Is this correct?

2) This problem I need some help starting it: Let M and N be sets with k and l elements, respectively. Determine the number of possible maps from M to N.

3) Find and example of the maps phi:M-->N and psi: N-->P such that Psi of Phi is surjective but phi is not surjective. For this problem I was thinking that I would need to find a map where phi is not surjective and a map where psi is bijective in order to get psi of phi to be bijective and phi not to be surjective. Any thoughts?

Thanks.

Update:
Would number 2 have an infinite number of maps between M--->N?

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