Prove that each of the following sets is equinumerous with N by defining (1) either an injection from the given set to N or a surjection from N to the given set, and (2) either injection from N to the given set, or a surjection from the given set to N. Implement the functions you define, in Python or another programming language.

1. N {(1,1)}

2. N {(1,1),...,(1,20)}

3. Z

4. N N

5. N N N

6. Q